How it works
The calculator evaluates the discriminant b² − 4ac and returns the real roots of ax² + bx + c = 0. A negative discriminant means the equation has no real roots.
Standard formula
x = (−b ± √(b² − 4ac)) / 2aWorked example
For x² − 5x + 6 = 0, the roots are 2 and 3 because (x − 2)(x − 3) = 0.
Frequently Asked Questions
What if a equals zero?
Then the equation is linear rather than quadratic, so enter a nonzero coefficient for this calculator.
What is the discriminant?
It is b² − 4ac and indicates whether the roots are two, repeated, or not real.
Where is the second root?
It appears in the result details below the main result.
Are complex roots shown?
No. This page focuses on real roots and reports when the discriminant is negative.