How to use the quadratic formula calculator
The quadratic formula solves ax² + bx + c = 0 when a is not zero. Enter the coefficients or the full equation to see the discriminant and both possible roots.
A useful method
- Put the equation in standard form and identify a, b, and c.
- Calculate the discriminant b² − 4ac.
- Substitute into x = (−b ± √(b² − 4ac)) / (2a) and simplify.
Worked example
Solve x² − 5x + 6 = 0
- Here a = 1, b = −5, and c = 6.
- The discriminant is (−5)² − 4(1)(6) = 1.
- The roots are (5 ± 1)/2.
Answer: x = 3 or x = 2.
Check your work
If b² − 4ac is negative, there are no real roots; the formula gives two complex roots instead.
Enter your own problem in the solver above and ask about any step you want explained.