What is a quadratic equation?
A quadratic equation is an equation whose highest variable exponent is two. Its standard form is ax² + bx + c = 0, where a is not zero.
Algebra
Quadratic Equation Solver
Solve quadratic equations, calculate the discriminant and find real or complex roots with a clear step-by-step solution in your browser.
Tool
Quadratic Equation Solver
Solve quadratic equations, calculate the discriminant and find real or complex roots with a clear step-by-step solution in your browser.
This tool runs in your browser. Your input is processed locally and is not uploaded.
About this Tool
Enter a quadratic equation in standard or expanded form to calculate its solutions. The solver identifies the coefficients, evaluates the discriminant and uses the quadratic formula to find two real roots, one repeated root or two complex roots. It also provides useful properties such as the vertex and axis of symmetry. Everything is calculated locally in your browser.
Examples
- x² - 5x + 6 = 0
- 2x² + 4x - 6 = 0
- x² + 6x + 9 = 0
- x² + 4x + 8 = 0
- 3x² = 12x
Frequently Asked Questions
What does the discriminant tell me?
The discriminant is b² - 4ac. A positive value produces two distinct real roots, zero produces one repeated real root and a negative value produces two complex conjugate roots.
Does the solver support complex solutions?
Yes. When the discriminant is negative, the solver displays the two roots using the imaginary unit i.
Does the equation need to be entered in standard form?
No. The solver can rearrange supported quadratic expressions into the standard form ax² + bx + c = 0 before identifying the coefficients.
What additional information does the solver provide?
Along with the roots, it can show the coefficients, discriminant, factorization when available, vertex and vertical axis of symmetry.
What happens when the quadratic coefficient is zero?
If the x² coefficient is zero, the expression is not quadratic. It should instead be solved as a linear equation.
Are the calculations performed online?
The tool works entirely in your browser. Your equation is not sent to a remote calculation service.