solve for x calculator

An equation is an algebraic equality involving one or more unknowns. Solving an equation is the same as determining that unknown or unknowns. The unknown is also called a variable. This equation calculator can solve equations with an unknown, the calculator can solve equations with variables on both sides and also equations with parentheses:

• Solving linear equation
• Solving quadratic equation
• Solving cubic equation
• Solving zero product equation
• Solving absolute value equation (equation with abs function)
• Solving exponential equation
• Solving logarithmic equation (equation involving logarithms)
• Solving trigonometric equation (equation involving cosine or sine)
• Solve online differential equation of first degree
• Solve online differential equation of the second degree

Solving linear equation online

A first-degree equation is an equation of the form `ax=b`. This type of equation is also called a linear equation. To solve these equations we use the following formula `x=b/a`.

linear equation solving of the form ax=b s is done very quickly, when the variable is not ambiguous, just enter equation to solve and then click solve, then the result is returned by solver. Details of calculations that led to the resolution of the linear equation are also displayed. To solve the linear equation following 3x+5=0, just type the expression 3x+5=0 in the calculation area, then click on "solve" button, result is returned `[x=-5/3]`.

• Step by step resolution of the equation : `3*x+5=0;x`


• Separating the terms which depend on the variable of those that do not depend on :
  `3*x = -5`


• Dividing by the variable coefficient :


• `x = -5/3`


• The solution of equation `3*x+5` is `[-5/3]`

Equations with variables on both sides

• Step by step resolution of the equation : `3*x+5=2*x;x`


• Separating the terms which depend on the variable of those that do not depend on :
  `x = -5`


• The solution of equation `3*x+5=2*x` is `[-5]`

Equations with parentheses

The calculator can solve equations with parentheses like this: `6*(3x+5)=5*(2x+3)`, just enter 6*(3x+5)=5*(2x+3) to get the result.

• Step by step resolution of the equation : `6*(3*x+5)=5*(2*x+3);x`


• Separating the terms which depend on the variable of those that do not depend on :
  `8*x = 15-30`


• Simplify :
  `8*x = -15`


• Dividing by the variable coefficient :


• `x = -15/8`


• The solution of equation `6*(3*x+5)=5*(2*x+3)` is `[-15/8]`

Equation with the variable in the denominator

• `(x-1)/(x^2-1)=0` returns the message no solution, domain definition is taken into account for the calculation, the numerator admits x = 1 as the root but the denominator is zero for x = 1 , 1 can't be a equation solution. The equation does not admit a solution.
• equation_solver(`1/(x+1)=3`) returns `[-2/3]`
• Step by step resolution of the equation : `1/(x+1)=3;x`


• The equation solving can be as follows `(-2-3*x)/(1+x)=0`


• We must find the values of x for which `-2-3*x=0` and `1+x!=0`


• Dividing by the variable coefficient :


• `x = -2/3`


• The denominator is not zero for `-2/3`, `-2/3` is a solution of the equation.


• The solution of equation `1/(x+1)=3` is `[-2/3]`

Solving quadratic equation online

A second-degree equation is an equation of the form `ax^2+bx+c=0`. This type of equation is also called a quadratic equation. To solve these equations the discriminant is calculated with the following formula `Delta=b^2-4ac`.
The discriminant is a number that determines the number of solutions of an equation.

• When the discriminant is positive, the equation of the second degree admits two solutions, which are given by the formula `(-b-sqrt(Delta))/(2a)` and `(-b+sqrt(Delta))/(2a)`;
• When the discriminant is null, the quadratic equation admits only one solution, it is said to be a double root, which is given by the formula  `(-b)/(2a)`;
• When the discriminant is negative, the polynomial equation of degree 2 admits no solution.

Solve quadratic equation online of the form has `ax^2+bx+c=0` is very quickly, when the variable is not ambiguous, just enter the equation to solve and click on the calculation, the result is returned. Steps of the calculations that led to the resolution of the quadratic equation are also displayed. To solve the quadratic equation following `x^2+2x-3=0`, just type the expression x^2+2x-3=0 in the calculation area, then click on calculate, the result is returned `[x=-3;x=1]`

• Step by step resolution of the equation : `x^2+2*x-3=0;x`


• The polynomial is of the form `a*x^2+b*x+c`, `a=1`, `b=2`, `c=-3`


• Its discriminant noted `Delta` (delta) is calculated with the following formula `Delta=(b^2-4ac)=(2)^2-4*(1)*(-3)=2^2-4*(-3)=16`


• The discriminant of the polynomial is equal to `16`


• The discriminant is positive, the equation has two solutions that are given by `x_1=(-b-sqrt(Delta))/(2a)` , `x_2=(-b+sqrt(Delta))/(2a)`.


• `x_1=(-b-sqrt(Delta))/(2a)=(-2-sqrt(16))/(2*1)=(-2-4)/(2*1)=-3`


• `x_2=(-b+sqrt(Delta))/(2a)=(-2+sqrt(16))/(2*1)=(-2+4)/(2*1)=1`.


• The solutions of the equation `x^2+2*x-3=0` are `[-3;1]`

Some examples of quadratic equation solver

• equation_solver(`1/(x+1)=1/3*x`) returns `[(-1+sqrt(13))/2;(-1-sqrt(13))/2]`
• `(x^2-1)/(x-1)=0` returns -1, the entire definition is taken into account for the calculation of the numerator admits two roots 1 and -1 but the denominator is zero for x = 1, 1 can not be the solution of equation.
• Step by step resolution of the equation : `(x^2-1)/(x-1)=0;x`


• Step by step resolution of the equation : `x^2-1=0;x`


• After calculation, the equation can be written : `x^2=1`
1. The equation is of the form `x^n=b`, with `n=2` and `b=1`
2. n is even, `b>0`, the equation admits two solutions that are `[1;-1]`


• The denominator is zero for `1`, `1` is not a solution to the equation.


• The solution of equation `(x^2-1)/(x-1)=0` is `[-1]`

Solving cubic equation

The equation calculator solves some cubic equations. In cases where the equation admits an obvious solution, the calculator is able to find the roots of a polynomial of the third degree. So the calculator will have no problem solving a third degree equation like this: equation_solver(`-6+11*x-6*x^2+x^3=0`).

• Step by step resolution of the equation : `-6+11*x-6*x^2+x^3=0;x`


• Finding an root of the polynomial `P(x) = -6+11*x-6*x^2+x^3`
1. P(1)=0, 1 is a root of the polynomial.
2. The polynomial can be written in the form `P(x)=(x-1)*(a*x^2+b*x+c)`
1. We can determine a, b, c by replacing the variable by 0, 2 and 3 and solving the system of 3 equations with 3 unknowns.
2. The system to be solved is `[-c=-6;a*4+b*2+c=0;2*(a*9+b*3+c)=0]`
3. The solution of the system is `[a=1;b=-5;c=6]`
4. The polynomial is written `P(x) = (x-1)*(6-5*x+x^2)`
3. Solving the following quadratic equation : `6-5*x+x^2`
• Step by step resolution of the equation : `6-5*x+x^2=0;x`


• The polynomial is of the form `a*x^2+b*x+c`, `a=1`, `b=-5`, `c=6`


• Its discriminant noted `Delta` (delta) is calculated with the following formula `Delta=(b^2-4ac)=(-5)^2-4*(1)*(6)=(-5)^2-4*6=1`


• The discriminant of the polynomial is equal to `1`


• The discriminant is positive, the equation has two solutions that are given by `x_1=(-b-sqrt(Delta))/(2a)` , `x_2=(-b+sqrt(Delta))/(2a)`.


• `x_1=(-b-sqrt(Delta))/(2a)=(--5-sqrt(1))/(2*1)=(--5-1)/(2*1)=2`


• `x_2=(-b+sqrt(Delta))/(2a)=(--5+sqrt(1))/(2*1)=(--5+1)/(2*1)=3`.


• The solutions of the equation `6-5*x+x^2` are `[2;3]`
4. The solutions of the cubic equation `-6+11*x-6*x^2+x^3=0` are `[2;3;1]`

Again, the solutions of the cubic equation will be accompanied by explanations which made it possible to find the result.

Solve an equation using the zero product property

The zero product property is used to solve equations of the form A*B=0 , that this equation is zero only if A = 0 or B = 0. To solve this type of equation can be done if A and B are polynomials of degree less than or equal to 2. The details of the calculations that led to the resolution of the equation is also displayed. It is also possible to solve the equations of the form `A^n=0`, if A is a lower degree of polynomial or equal to 2.

Some examples of solving equations using the zero product property.

• equation_solver(`(x+1)(x-4)(x+3)=0;x`) returns `[-1;4;-3]`
• `(x^2-1)(x+2)(x-3)=0` returns `[1;-1;-2;3]`.

• Step by step resolution of the equation : `(x^2-1)*(x+2)*(x-3)=0;x`


• Equation product: A*B=0 if A=0 or B=0


• Step by step resolution of the equation : `(x^2-1)*(x+2)=0;x`


• Equation product: A*B=0 if A=0 or B=0


• Step by step resolution of the equation : `x^2-1=0;x`


• After calculation, the equation can be written : `x^2=1`
1. The equation is of the form `x^n=b`, with `n=2` and `b=1`
2. n is even, `b>0`, the equation admits two solutions that are `[1;-1]`


• Step by step resolution of the equation : `x+2=0;x`


• Separating the terms which depend on the variable of those that do not depend on :
  `x = -2`


• The solution of equation `x+2` is `[-2]`


• The solutions of the equation `(x^2-1)*(x+2)` are `[1;-1;-2]`


• Step by step resolution of the equation : `x-3=0;x`


• Separating the terms which depend on the variable of those that do not depend on :
  `x = 3`


• The solution of equation `x-3` is `[3]`


• The solutions of the equation `(x^2-1)*(x+2)*(x-3)=0` are `[1;-1;-2;3]`

Solve absolute value equation

The solver allows to solve equation involving the absolute value it is able to solve linear equations using absolute values, quadratic equations involving absolute values but also other many types of equation with absolute values.

Here are two examples of using the equation calculator to solve an equation with an absolute value:

• `abs(2*x+4)=3`, solver shows details of the calculation of an linear equation with absolute value.
• `abs(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with absolute value.

• Step by step resolution of the equation : `abs(x^2-4)=4;x`


• We assume that `x^2-4>0`, so `|x^2-4|=x^2-4`, we solve the equation `x^2-4=4`.


• Step by step resolution of the equation : `x^2-4=4;x`


• After calculation, the equation can be written : `x^2=8`
1. The equation is of the form `x^n=b`, with `n=2` and `b=8`
2. n is even, `b>0`, the equation admits two solutions that are `[2*sqrt(2);-2*sqrt(2)]`


• We assume that `x^2-4<0`, so `|x^2-4|=-(x^2-4)=4-x^2`, we solve the equation `4-x^2=4`.


• Step by step resolution of the equation : `4-x^2=4;x`


• The polynomial is of the form `a*x^2+b*x+c`, `a=-1`, `b=0`, `c=0`


• Its discriminant noted `Delta` (delta) is calculated with the following formula `Delta=(b^2-4ac)=(0)^2-4*(-1)*(0)=0=0`


• The discriminant of the polynomial is equal to `0`


• The discriminant is zero, the equation has a solution that is given by `x=(-b)/(2a)`.


• `x=(-b)/(2a)=(-0)/(2*-1)=0`


• The solution of equation `4-x^2=4` is `[0]`


• The solutions of the equation `abs(x^2-4)=4` are `[2*sqrt(2);-2*sqrt(2);0]`

Solve exponential equation

The equation calculator allows to solve equation involving the exponential it is able to solve linear equations using exponential, quadratic equations involving exponential but also other many types of equation with exponential.

Here are two examples of using the calculator to solve an equation with an exponential:

• `exp(2*x+4)=3`, solver shows details of the calculation of an linear equation with exponential.
• `exp(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with exponential.

• Step by step resolution of the equation : `exp(x^2-4)=4;x`


• We take the logarithm of each side of the equation it is therefore necessary to solve the following equation : `x^2-4=ln(4)`


• Step by step resolution of the equation : `x^2-4=ln(4);x`


• After calculation, the equation can be written : `x^2=4+ln(4)`
1. The equation is of the form `x^n=b`, with `n=2` and `b=4+ln(4)`
2. n is even, `b>0`, the equation admits two solutions that are `[sqrt(4+ln(4));-sqrt(4+ln(4))]`


• The solutions of the equation `exp(x^2-4)=4` are `[sqrt(4+ln(4));-sqrt(4+ln(4))]`

Solve logarithmic equation

Solve logarithmic equation ie some equations involving logarithms is possible. In addition to providing the result, the calculator provides detailed steps and calculations that led to the resolution of the logarithmic equation. To solve the following equation logarithmic ln(x)+ln(2x-1)=0, just type the expression in the calculation area, then click on the calculate button.

• Step by step resolution of the equation : `ln(x)+ln(2*x-1)=0;x`


• Using the properties of the natural logarithm, `ln(a)+ln(b)=ln(ab)`, `a*ln(b)= ln(b^a)`


• The solutions can be determined from the following equation : `-x+2*x^2=exp(0)`


• Step by step resolution of the equation : `-x+2*x^2=exp(0);x`


• The polynomial is of the form `a*x^2+b*x+c`, `a=2`, `b=-1`, `c=-1`


• Its discriminant noted `Delta` (delta) is calculated with the following formula `Delta=(b^2-4ac)=(-1)^2-4*(2)*(-1)=(-1)^2+4*2=9`


• The discriminant of the polynomial is equal to `9`


• The discriminant is positive, the equation has two solutions that are given by `x_1=(-b-sqrt(Delta))/(2a)` , `x_2=(-b+sqrt(Delta))/(2a)`.


• `x_1=(-b-sqrt(Delta))/(2a)=(--1-sqrt(9))/(2*2)=(--1-3)/(2*2)=-1/2`


• `x_2=(-b+sqrt(Delta))/(2a)=(--1+sqrt(9))/(2*2)=(--1+3)/(2*2)=1`.


• The solutions of the equation `-x+2*x^2=exp(0)` are `[-1/2;1]`


• `-1/2` is not in the domain of definition, it is not a solution of equation `ln(x)+ln(2*x-1)=0`.


• The solution of equation `ln(x)+ln(2*x-1)=0` is `[1]`

Solving trigonometric equation

The equation calculator allows to solve circular equations, it is able to solve an equation with a cosine of the form cos(x)=a or an equation with a sine of the form sin(x)=a. Calculations to obtain the result are detailed, so it will be possible to solve equations like `cos(x)=1/2` or `2*sin(x)=sqrt(2)` with the calculation steps.

• Step by step resolution of the equation : `2*sin(x)=sqrt(2);x`


• Dividing each member of the equation by `2`


• We obtain : `sin(x)=sqrt(2)/2`


• We know that `sin(pi/4)=sqrt(2)/2`


• With, `k in ZZ`


• The solutions of the equation `2*sin(x)=sqrt(2)` are `[x=2*k*pi+pi/4;x=(3*pi)/4+2*k*pi]`

Solving first order linear differential equation

The function equation_solver can solve first order linear differential equations online, to solve the following differential equation : y'+y=0, you must enter equation_solver(`y'+y=0;x`).

Solving second order differential equation

The function equation_solver can solve second order differential equation online, to solve the following differential equation : y''-y=0, you must enter equation_solver(`y''-y=0;x`).

Games and quizzes on equation solving

To practice the different calculation techniques, several quizzes on solving equations are proposed.