Quadratic Equation Calculator
Solve equations of the form ax² + bx + c = 0. This shows the discriminant, the roots (real or complex), and the formula used.
| a | coefficient of x² |
| b | coefficient of x |
| c | constant |
Result
Roots will appear here.
How it works
A quadratic equation graphs as a parabola. Its roots are the x-values where the expression equals zero (where the parabola crosses the x-axis, if it does).
Formula and steps
- Standard form: ax² + bx + c = 0
- Compute the discriminant: D = b² − 4ac
- Apply the quadratic formula: x = (−b ± √D) / (2a)
- If D > 0 → two different real roots. If D = 0 → one real root (a repeated/double root). If D < 0 → two complex roots: x = (−b / 2a) ± (√(−D) / 2a)i.
- If a = 0 the equation is linear (bx + c = 0), so x = −c/b when b ≠ 0.
Worked example
For x² − 3x + 2 = 0 (a=1, b=−3, c=2): D = 9 − 8 = 1, so x = (3 ± 1)/2 giving x = 2 and x = 1. (It factors as (x−1)(x−2)=0.)
Results are estimates based on the inputs and assumptions shown. Check units and inputs, and verify consequential decisions with an authoritative source or qualified professional.
How to use the Quadratic Equation Calculator
It takes a few seconds, and every figure is calculated in your browser.
- Enter the coefficient a.
- Enter the coefficient b.
- Enter the coefficient c.
- Press Calculate — the result appears in the dark panel beside the form.
- Use Copy, CSV, Share or Print under the result if you want to keep it.
Quadratic Equation Calculator — frequently asked questions
What formula does the Quadratic Equation Calculator use?
Standard form: ax² + bx + c = 0 Compute the discriminant: D = b² − 4ac Apply the quadratic formula: x = (−b ± √D) / (2a) If D > 0 → two different real roots. If D = 0 → one real root (a repeated/double root). If D < 0 → two complex roots: x = (−b / 2a) ± (√(−D) / 2a)i. If a = 0 the equation is linear (bx + c = 0), so x = −c/b when b ≠ 0.
How does the Quadratic Equation Calculator work?
A quadratic equation graphs as a parabola. Its roots are the x-values where the expression equals zero (where the parabola crosses the x-axis, if it does).
Can you walk through a worked example?
For x² − 3x + 2 = 0 (a=1, b=−3, c=2): D = 9 − 8 = 1, so x = (3 ± 1)/2 giving x = 2 and x = 1. (It factors as (x−1)(x−2)=0.)
Last updated 10 November 2026 · Formula, worked example and assumptions are documented above, and every result is calculated in your browser.