Quadratic Formula Calculator

Quadratic Formula Calculator

Solve quadratic equations in standard form and find the real or complex roots from the discriminant.

Last updated: June 2026 | By Patchworkr Team

Roots
3 , 2
x = 3 and x = 2
Discriminant1
Nature of rootsTwo real roots
Calculation steps
Equation: 1x^2 + (-5)x + (6) = 0
Discriminant: D = b^2 - 4ac = (-5)^2 - 4(1)(6) = 1
D > 0, so there are two real roots.
x = (-b +/- sqrt(D)) / (2a)
x1 = 3
x2 = 2
Standard form
ax^2 + bx + c = 0
What the result panel shows
The discriminant tells us whether the roots are real or complex, and the root panel updates from the current coefficient values.

What Is The Quadratic Formula?

The quadratic formula solves equations written in the form ax^2 + bx + c = 0. It is one of the most common ways to find the x-intercepts of a parabola.

The discriminant D = b^2 - 4ac determines how many solutions the equation has. Positive values give two real roots, zero gives one repeated real root, and negative values give two complex roots.

How To Solve A Quadratic Equation

  1. Write the equation in standard form: ax^2 + bx + c = 0.
  2. Identify the coefficients a, b, and c.
  3. Compute the discriminant D = b^2 - 4ac.
  4. Substitute the values into the quadratic formula and simplify.
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

Worked Example

For x^2 - 5x + 6 = 0, the coefficients are a = 1, b = -5, and c = 6.

D = (-5)^2 - 4(1)(6) = 25 - 24 = 1
x = (5 +/- 1) / 2
x = 3 and x = 2

Frequently Asked Questions

Can the coefficient a be zero?

No. If a is zero, the equation is linear rather than quadratic.

What does the discriminant tell me?

It tells you whether the quadratic has two real roots, one repeated real root, or two complex roots.

Does the calculator support complex roots?

Yes. When the discriminant is negative, the result panel shows the complex roots.

Can I use decimal coefficients?

Yes. The calculator accepts decimal values for a, b, and c.

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