Quadratic Equation Solver
Solve ax² + bx + c = 0 and see the roots and discriminant.
Solve any quadratic equation ax² + bx + c = 0 by entering the coefficients a, b, and c. The solver shows both roots (or the double root), plus the discriminant so you can see at a glance whether the roots are real.
How it's calculated
Roots come from the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac tells the story: positive means two real roots, zero means one double root, negative means no real roots.
Frequently asked questions
How do I solve x² − 5x + 6 = 0?
Enter a=1, b=−5, c=6. The roots are x = 2 and x = 3, because (x−2)(x−3) expands to x² − 5x + 6.
What does the discriminant tell me?
The discriminant b²−4ac predicts the roots before you compute them: if it's positive there are two real roots, if zero there's one repeated root, and if negative there are no real roots.
What if a is zero?
Then it's not quadratic — it's the linear equation bx + c = 0, and the solver gives the single root x = −c/b.