Math & Statistics
Quadratic Formula Calculator
Solve ax² + bx + c = 0 and report the discriminant, real roots, or complex-root components. The calculator uses x = (−b ± √(b² − 4ac)) ÷ 2a. It returns more than one result so you can check the main answer against a useful secondary measure. The discriminant determines whether the equation has two real roots, one repeated root, or a complex pair. Very large coefficients can lose floating-point precision; rescale the equation when possible.
Check the displayed units, assumptions, and rounding before relying on the result.
Calculate and compare
Use the number box for precision or the slider for fast scenario testing.
Scenario results
First root
3
Uses the plus branch.
Second root
2
Uses the minus branch.
Discriminant
1
Two real roots.
How the calculation works
Use consistent units and retain full precision until the final display step.
Worked example
Reproduce the displayed scenario, then change one assumption at a time.
Assumptions behind the result
- • Inputs use the units shown beside each control.
- • The displayed formula is applied without hidden market or demographic data.
- • Rounding occurs only for display; calculations keep full numeric precision.
- • The discriminant determines whether the equation has two real roots, one repeated root, or a complex pair.
- • Very large coefficients can lose floating-point precision; rescale the equation when possible.
Mistakes that change the answer
- • Mixing percentages with decimals or mixing incompatible units.
- • Relying on a rounded intermediate value instead of the full result.
- • Changing several assumptions at once instead of testing coefficient a separately.