Quadratic Equation Solver
Solve ax² + bx + c = 0 with real or complex roots, discriminant and vertex.
How to use the Quadratic Equation Solver
Enter coefficients a, b and c. The solver shows both roots, the discriminant, the vertex and the axis of symmetry.
Formula
x = [−b ± √(b² − 4ac)] ÷ 2a
Worked example
x² − 3x − 10 = 0 has roots x = 5 and x = −2.
Frequently asked questions
What does the discriminant tell me?
If b² − 4ac > 0 there are two real roots; = 0 one repeated root; < 0 two complex roots.
Results are estimates for educational and planning purposes. Always confirm important financial, health or legal decisions with a qualified professional. Last reviewed 2026-09-27.