Quadratic equation solver
Solve the quadratic equation ax² + bx + c = 0: calculate the discriminant, roots and parabola vertex.
ax² + bx + c = 0
Calculations are based on Estonia's tax rates in force for 2026. Results are informational.
Last updated: 2026-06-03
How to solve a quadratic equation?
A quadratic equation is solved with x = (−b ± √D) / 2a, where the discriminant D = b² − 4ac. If D > 0 there are two roots, if D = 0 one root, and if D < 0 there are no real roots.
How it is calculated
Formula
ax² + bx + c = 0. Discriminant D = b² − 4ac. Roots x = (−b ± √D) ÷ (2a). D > 0 two roots, D = 0 one, D < 0 no real roots.
Example
x² − 5x + 6 = 0 → D = 1 → x = 3 and x = 2.
Frequently asked questions
How do I solve a quadratic equation?+
Use the formula x = (−b ± √D) ÷ (2a), where the discriminant D = b² − 4ac.
What does the discriminant tell me?+
If D > 0 there are two real roots, if D = 0 one root, and if D < 0 there are no real roots.