The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.

Equation 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:

1. Solving linear equation
2. Solving quadratic equation
3. Solving cubic equation
4. Solving zero product equation
5. Solving absolute value equation (equation with abs function)
6. Solving exponential equation
7. Solving logarithmic equation (equation involving logarithms)
8. Solving trigonometric equation (equation involving cosine or sine)
9. Solve online differential equation of first degree
10. 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]`. it is also possible to solve equations the form of `(ax+c)/g(x)=0` or equations that may be in this form , g(x) represents a function. When you enter an expression without '=' sign; the function returns when possible values ​​for which expression is zero. For example, enter x+5 and resolve back to x+5=0 and solve.

Equations with variables on both sides

The calculator can solve equations with variables on both sides like this: `3x+5=2x`, just enter 3x+5=2x to get the result.

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.

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]`

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]`
To solve an equation with variables on both sides of the equality using the calculator, like this one `x^2+x=2x^2+4x+1`, just type the expression x^2+x=2x^2+4x+1 in the calculation area, then click on calculate, the result is returned `[x=(-3+sqrt(5))/2;x=(-3-sqrt(5))/2]`
It is also possible to solve the equations of the form `(ax^2+bx+c)/g(x)=0` or equations that may be in this form, g(x) represents a function.

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.

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`).

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]`.

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.

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.

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.

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.

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.

Syntax :

equation_solver(equation;variable), variable parameter may be omitted when there is no ambiguity.

Examples :

Equation resolution of first degree

• equation_solver(`3*x-9`) is equal to write equation_solver(`3*x-9=0;x`) the returned result is 3.
• equation_solver(`3*x+3=5*x+2`) returns `1/2`

Solving quadratic equations

• Solving the equation `2*x^2-2=x^2+x` with the function equation_solver(`2*x^2-2=x^2+x`) returns two solutions separated by a semicolon [x=-1;x=2]

Solving cubic equations

• Solving the equation `-6+11*x-6*x^2+x^3=0` with the function equation_solver(`-6+11*x-6*x^2+x^3=0`) returns three solutions.

Solve differential equation

• equation_solver(`y'+y=0;x`) returns `[y=k*exp(-x)]` k represents a constant.
• equation_solver(`y''-y=0;x`) returns `[y=a*exp(-x)+b*exp(x)]` a and b are constants.