Quadratic equation calculator (step by step)

Q: How do you calculate the discriminant?

The discriminant is Δ = b² − 4ac. If it is positive there are two solutions, if it is zero there is a double solution, and if it is negative there are no real solutions.

Q: What happens if a = 0?

If a = 0, the equation is no longer quadratic and becomes linear (bx + c = 0). This calculator requires a to be non-zero.

Q: Is the calculator free?

Yes, the quadratic equations calculator is free. And if you want to practice with hundreds of instantly corrected exercises, you have a 5-day trial with no card required on Refuerzo.ai.

a·x² + b·x + c = 0

a

b

c

Practice exercises on ecuaciones de segundo grado

How how to solve a quadratic equation

A quadratic equation has the form ax² + bx + c = 0. It is solved using the quadratic formula x = (−b ± √(b² − 4ac)) / 2a.

The discriminant Δ = b² − 4ac indicates the number of solutions: two if Δ > 0, one (double) if Δ = 0, and none real if Δ < 0.

ExampleSolve x² − 5x + 6 = 0.

Step-by-step solution

a = 1, b = −5, c = 6.
Δ = (−5)² − 4·1·6 = 25 − 24 = 1.
x = (5 ± √1) / 2 = (5 ± 1) / 2.

Solutions: x = 3 and x = 2.

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With Refuerzo.ai you practice quadratic equations with hundreds of exercises and instant feedback that explains why. Try for free, no card required.

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Frequently asked questions

How do you calculate the discriminant?

The discriminant is Δ = b² − 4ac. If it is positive there are two solutions, if it is zero there is a double solution, and if it is negative there are no real solutions.

What happens if a = 0?

If a = 0, the equation is no longer quadratic and becomes linear (bx + c = 0). This calculator requires a to be non-zero.

Is the calculator free?

Yes, the quadratic equations calculator is free. And if you want to practice with hundreds of instantly corrected exercises, you have a 5-day trial with no card required on Refuerzo.ai.