Equation Solver: Linear and Quadratic
This equation solver finds the solutions of an equation in one variable. Type something like 2x + 3 = 11, x^2 - 5x + 6 = 0, x^3 - 6x^2 + 11x - 6 = 0 or even cos(x) = x. Polynomial equations up to degree four, and higher when rational roots exist, are solved exactly, with complex roots shown when there are no real ones. Other equations are searched numerically between -100 and 100. It all runs in your browser with no sign-up.
Equation Solver
Solve linear, quadratic, cubic, quartic and other equations for free.
How to use the Equation Solver
- Type the equation with an equals sign, for example x^2 = 9 or 3x - 7 = 2x + 5.
- Enter the letter to solve for if the equation has more than one variable.
- Read the solutions in the result box.
- Review the rewritten equation and discriminant shown below to check the method.
Methods used
Linear: x = −b / a. Quadratic: x = (−b ± √(b² − 4ac)) / 2a. Higher degrees: rational root test, then the quadratic formula or a numerical root finder. Other equations: scan for sign changes and refine by bisection.
Features
- Linear, quadratic, cubic and quartic equations
- Exact fractions and roots where possible
- Complex roots when no real roots exist
- Numerical search for other equations
- Solve a formula for one letter
- Free with no sign-up
Frequently asked questions
How do I solve a quadratic equation?
Type it, for example x^2 - 5x + 6 = 0. The solver computes the discriminant, then shows the exact roots, such as 2 and 3, or a decimal form when the roots are irrational.
Can the equation solver find complex answers?
Yes. When the discriminant is negative, or when higher-degree polynomials have no real root, it shows the complex roots in the form a ± bi.
What about equations that are not polynomials?
Equations such as cos(x) = x are solved numerically by scanning for sign changes between -100 and 100. The answers are rounded and any roots outside that range are not shown.
Can it solve for a letter in a formula?
Yes, if the equation is linear in that letter. For example, 2x + 3y = 7 solved for x gives x = (7 - 3y)/2.
Why does it say no solution?
The equation may be a contradiction such as x + 1 = x, or it may have no real solution in the searched range. Check the equation for typing mistakes.