Δ Quadratic Formula Calculator
Every quadratic equation ax² + bx + c = 0 is solved by one famous formula: x = (−b ± √b²−4ac) / 2a. The part under the root — the discriminant — decides everything: positive means two roots, zero means one repeated root, negative means no real roots.
Type the three coefficients a, b and c. The calculator shows the discriminant first, then the roots, so you can follow the same steps you would do by hand.
How to use this calculator
Type the coefficients a, b and c of your equation ax squared + bx + c = 0, then press Calculate.
- Type the coefficient of x squared into the Coefficient a field; it cannot be zero.
- Type the coefficient of x into the Coefficient b field.
- Type the constant term into the Constant c field.
- Press Calculate and read the discriminant first, then the roots underneath it.
Frequently asked questions
What does this quadratic formula calculator solve?
Any equation of the form ax squared + bx + c = 0. It applies the quadratic formula x = (-b plus or minus root(b squared - 4ac)) / 2a and shows every step that matters: the discriminant and the roots.
What does the discriminant tell me?
The discriminant b squared - 4ac decides the outcome before you finish: positive means two distinct real roots, zero means one repeated root, and negative means no real roots, only complex ones.
Can you show a worked example?
For x squared - 3x + 2 = 0, the coefficients are 1, -3, 2. The discriminant is 9 - 8 = 1, and the roots are (3 + 1)/2 = 2 and (3 - 1)/2 = 1.
Why does it reject a = 0?
With a = 0 the x-squared term vanishes and the equation becomes linear, bx + c = 0, which the quadratic formula cannot solve. That case needs a linear equation solver instead.