Quadratic Equation Solver
Solve any quadratic equation of the form ax² + bx + c = 0. The solver shows both roots (real or complex), the discriminant and the vertex of the parabola.
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Result
Two distinct real roots (discriminant > 0).
How to use
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Save ⟶How to use the Quadratic Equation Solver
- 1Enter a (coefficient of x²) in the form on the left.
- 2Fill in the remaining fields — the result updates automatically as you type.
- 3Review the highlighted result and the supporting breakdown on the right.
- 4Use Copy, Share or Print to save or send your result.
The quadratic formula
Any equation ax² + bx + c = 0 is solved by x = (−b ± √(b² − 4ac)) / 2a. The expression under the square root, b² − 4ac, is the discriminant: positive means two real roots, zero means one repeated root, negative means a pair of complex conjugate roots.
Geometrically, the roots are where the parabola y = ax² + bx + c crosses the x-axis, and the vertex (−b/2a, c − b²/4a) is its highest or lowest point. Try plotting your equation in our free Graphing Calculator to see it.
Frequently Asked Questions
▸What does a negative discriminant mean?
The equation has no real solutions — the parabola never touches the x-axis. The two solutions are complex numbers of the form p ± qi.
▸Can I solve a quadratic by factoring instead?
Yes, when the roots are rational. The quadratic formula always works, including for irrational and complex roots.