Solve any quadratic equation in the form ax^2 + bx + c = 0. Enter the three coefficients to get both roots instantly, including complex roots when the discriminant is negative.
Quadratic Formula Calculator
LiveRoots
x = 3, 2
Discriminant
1
Root type
Two real roots
Works for a not equal to 0. If a = 0, it's a linear equation instead.
The quadratic formula
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a
Example
x^2 - 5x + 6 = 0: a=1, b=-5, c=6. Discriminant = 25 - 24 = 1. x = (5 +/- 1) / 2 = 3 and 2.
Step-by-step guide
- Enter the coefficients a, b, and c from your equation in the form ax^2 + bx + c = 0.
- Check the discriminant (b^2 - 4ac) - positive means two real roots, zero means one repeated root, negative means two complex roots.
- Read the roots shown in the result.
Common mistakes
Mixing up the sign of b - if your equation is x^2 - 5x + 6, then b is -5, not 5.
Forgetting the plus-or-minus - a quadratic equation generally has two solutions, not one.
Frequently asked questions
What does a negative discriminant mean?
It means the equation has no real solutions - the roots are complex numbers, involving the imaginary unit i. Graphically, this means the parabola never crosses the x-axis.
What if a = 0?
If a is 0, the equation isn't quadratic anymore - it becomes linear (bx + c = 0), which has at most one solution and needs a different approach.
Can I check my answer?
Yes - substitute each root back into the original equation. If it's correct, the equation should equal zero.
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