Using the Quadratic Formula Calculator
Move every term to one side before entering the coefficients. A missing x term means b is zero, while a missing constant means c is zero. Keep the sign attached to each coefficient.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- a
- 1
- b
- -5
- c
- 6
Example result
- Discriminant
- 1
- Root 1
- 3
- Root 2
- 2
Method and assumptions
Roots = (−b ± √(b² − 4ac)) / (2a). A stable rearrangement avoids cancellation.
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
What does a negative discriminant tell me?
The equation has no real roots, but it has complex roots. The calculator writes them using i, whose square is −1, rather than treating the equation as unsolvable.
Guide updated .