Quadratic Equation Solver
Solve ax² + bx + c = 0 — discriminant, real or complex roots, vertex and full working.
Result
How to use
- 1
Enter the coefficients a, b and c of ax² + bx + c = 0.
- 2
See the discriminant, the roots and the vertex.
- 3
Scroll down for the step-by-step working.
Questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the root, D = b² − 4ac, is called the discriminant.
What does the discriminant tell me?
D > 0: two different real roots. D = 0: one repeated real root. D < 0: no real roots — two complex (imaginary) roots.
What is the vertex?
The turning point of the parabola y = ax² + bx + c, at x = −b ÷ 2a. It is the minimum when a > 0 and the maximum when a < 0.
About this Quadratic tool
Quadratic Equation Solver — Solve ax² + bx + c = 0 — discriminant, real or complex roots, vertex and full working. It is one of 200 free tools on namasivayam.in, made by software engineer Namasivayam Vadivelan for everyday use in India.
Everything is calculated instantly in your browser: nothing you type or upload is sent to any server, there is no sign-up, and it works on mobile and desktop. Enter the coefficients a, b and c of ax² + bx + c = 0.
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Results are estimates to help you plan. They are not financial, tax or medical advice.