Quadratic Equation Solver
Solve ax²+bx+c=0 online — enter the coefficients to get the discriminant and the roots instantly.
ax² + bx + c = 0
How to solve a quadratic equation
A quadratic equation has the standard form ax²+bx+c=0, where a, b, and c are numeric coefficients and a is not zero. Enter your coefficients in the fields above and the solver immediately returns the discriminant and the roots.
The solution relies on the discriminant D = b²−4ac. When D is greater than zero there are two distinct real roots, when D equals zero there is one root, and when D is less than zero there are no real roots, only a pair of complex ones.
Every calculation runs locally in your browser and updates instantly — nothing is uploaded to a server, so your work stays private and the solver even works offline.
Why use this solver
Complete solution
Shows the discriminant and both roots, not just the final answer.
Instant results
Roots recompute automatically the moment you change any coefficient.
Any coefficients
Handles fractional and negative values of a, b, and c.
Frequently asked questions
What is the discriminant of a quadratic equation?
The discriminant is the expression D = b²−4ac. Its sign tells you the number of real roots: two when D>0, one when D=0, and none when D<0.
What is the quadratic formula for the roots?
The roots are found with x = (−b ± √D) / (2a), where D = b²−4ac. The plus sign gives the first root and the minus sign the second.
What happens when the discriminant is negative?
When D<0 there are no real roots, but there are two complex roots of the form x = (−b ± i√|D|) / (2a). The solver will report that the equation has no real solutions.
Why can't coefficient a be zero?
If a=0 the x² term disappears and the equation becomes linear (bx+c=0) rather than quadratic. A quadratic equation therefore requires a to be non-zero.
Can I enter fractional or negative coefficients?
Yes. The fields accept whole and decimal numbers, including negatives — for example a=1.5, b=−4, c=2.