How to use the Quadratic Equation Solver
- Write your equation in the form ax² + bx + c = 0.
- Enter the coefficients a, b and c (use negative numbers where needed).
- Read the roots, then the discriminant and vertex below.
What does this tool do?
The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a solves every quadratic equation. The part under the square root, the discriminant, tells you what kind of answer to expect: positive means two real roots, zero means one repeated root, and negative means two complex roots.
The solver also gives the vertex — the turning point of the parabola — and whether the curve opens upward or downward, which is handy for graphing and optimisation problems.
Why use it?
- Handles complex roots, not just real ones.
- Shows the discriminant and vertex at the same time.
- Falls back to a linear solve if a = 0.
Example
For x² − 3x + 2 = 0: D = 9 − 8 = 1, so x = (3 ± 1) ÷ 2, giving x = 2 and x = 1. The vertex is at (1.5, −0.25).
The formula
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
What if a is 0?
Then it isn't a quadratic. The solver treats it as the linear equation bx + c = 0 and solves that instead.
What does a complex root mean?
The parabola never crosses the x-axis. The roots are written as p ± qi, where i is the square root of −1.
Last reviewed by the M2Toolkit team.