What if a equals zero?

If a = 0 the equation is linear (bx + c = 0), not quadratic. The calculator will show an error and ask you to enter a non-zero value for a.

What does a negative discriminant mean?

A negative discriminant means the equation has no real solutions. Instead, two complex conjugate roots of the form a ± bi are returned, where i is the imaginary unit (√−1).

Can this handle decimal and negative coefficients?

Yes. You can enter any real number for a, b, and c — including negatives, decimals, and fractions expressed as decimals.

What is the quadratic formula?

The quadratic formula is x = (−b ± √(b²−4ac)) / (2a). It gives both roots of ax²+bx+c=0 directly from the coefficients without factoring.

How accurate are the results?

Results are computed using JavaScript's double-precision floating-point arithmetic and rounded to 8 significant figures for display. For integer or simple fractional inputs the results are exact.

Quadratic Formula Calculator

Name: Quadratic Formula Calculator
Availability: InStock
Author: Nham Vu

Enter coefficients a, b, and c to solve ax²+bx+c=0 and instantly see both roots, the discriminant, and step-by-step working.

Enter Coefficients

ax² + bx + c = 0

a — coefficient of x² (must not be zero)

b — coefficient of x

c — constant term

Try an example

Enter coefficients and press Solve

Results and step-by-step working will appear here.

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Summary

Enter coefficients a, b, and c to solve ax²+bx+c=0 and instantly see both roots, the discriminant, and step-by-step working.

How it works

Enter the coefficient a (must not be zero), b, and c for your equation.
The calculator computes the discriminant Δ = b² − 4ac.
If Δ > 0, two distinct real roots are returned.
If Δ = 0, one repeated real root is returned.
If Δ < 0, two complex conjugate roots are returned in a±bi form.
Full step-by-step working is displayed so you can verify each calculation.

Use cases

Homework and exam prep for algebra, pre-calculus, or calculus courses.
Quickly checking manually solved quadratic equations.
Finding the x-intercepts (zeros) of a parabola.
Solving physics and engineering problems modeled by quadratic equations.
Teaching the quadratic formula with live step-by-step feedback.
Verifying factored forms of quadratic expressions.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu