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\(y = ax^2 + bx + c\)


When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\)

Warning! a must be different from zero.

1/ The Equation


2/ The Discriminant


There is one solution.

There are two real solutions.

There are two imaginary solutions.

3/ Resolution


4/ Solution(s)


Discover our Quadratic formula calculator, our online program solver will allow you to solve quadratic equation to reconcile you with work.

To help you understand our quadratic equation solving calculator, here is a course that will inform you about our calculation methods.

Step 1: Calculate the delta

The resolution of a quadratic equation necessarily passes by the calculation of the discriminant also called delta. This calculation allows us to know the number of solutions to the equation, namely that if:

  • Δ
  • Δ = 0: There is an unique solution
  • Δ > 0: the resolution contains 2 solutions

To calculate the delta, you must apply the formula Δ = b²-4ac

Step 2: How the Quadratic Formula Calculator works?

Once you know the number of solutions to your equation, you can solve it by using the following formula:

X = (- b ± √ (b ^ 2-4ac)) / 2a

You can now solve your equation and verify your results using our calculator. Do not hesitate to use our tool for your work. Whether your work is complex, one or two unknowns, you can check your calculations with Calculator Market.

Step 3: Reminder for the Quadratic Equations

A quadratic equation always has the form ax2 + bx + c = 0 with a ≠ 0.
As with the linear equations, the remarkable identities will simplify the resolution. Thus, we invite you to memorize the following remarkable identities:

  • A² + 2ab + b² = (a + b) ²
  • A²-b² = (a + b) (a-b)
  • A²-2ab + b² = (a-b) ²

You are now armed to solve a quadratic equation by yourself. Our quadratic formula calculator takes all the steps and details the results until you get the solutions. Thus, you will find 4 steps after entering the data in fields a, b and c:

  1. Equation: Resumes the total formatting of your second degree equation.
  2. The Discriminant (delta): That will let you know the number of solutions.
  3. Resolution: For all calculation steps.
  4. Solution (s): Achieving the long-awaited result.