Formula and method
Formulax = (−b ± √(b² − 4ac)) ÷ 2a.
The discriminant determines whether the equation has two, one or no real roots.
Worked example
x² − 5x + 6 = 0 has roots 2 and 3.
How to use this calculator
- Enter the values using the labels and units shown.
- Review the live result and supporting details.
- Check the formula, example and assumptions before using the answer.
Assumptions and limits
- Coefficient a must not be zero.
- This page reports real roots only.
Reference
Formula reviewed 2026-07-15