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Calculators / Math / Quadratic equation
Quadratic equation calculator
Find the real roots of ax² + bx + c = 0.
On this page
First root3
Second root2
Discriminant1
Calculator controls
How to calculate
Find the real roots of ax² + bx + c = 0.
x = (−b ± √(b² − 4ac)) ÷ 2a
Worked example
Coefficient a: 1; Coefficient b: -5; Coefficient c: 6.
First root: 3 ; Second root: 2 ; Discriminant: 1 .
Assumptions and limits
Displays real roots only. a must be nonzero.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Roots are the x values where ax² + bx + c equals zero. The discriminant tells you whether the equation has two, one repeated, or no real roots.
When this tool is useful
Check a factorization or solve a simple quadratic model.
Understanding your inputs
| Input | What to enter |
|---|---|
| Coefficient a | Enter a number of at least -1000000 and no more than 1000000. |
| Coefficient b | Enter a number of at least -1000000 and no more than 1000000. |
| Coefficient c | Enter a number of at least -1000000 and no more than 1000000. |
Frequently asked questions
What does a negative discriminant mean?
The equation has complex roots rather than real roots. This calculator reports that there are no real roots; it does not display complex values.
Why must a be nonzero?
If a is zero, the x² term disappears and the expression is linear, not quadratic. Solve bx + c = 0 instead.