Quadratic Formula Calculator

The Quadratic Formula Calculator helps you quickly solve any quadratic equation of the form ax² + bx + c = 0. Just enter the values of a, b, and c, and get the exact real or complex roots instantly.

How to Use the Calculator

1. Enter the coefficient a (the number in front of x²).
2. Enter the coefficient b (the number in front of x).
3. Enter the constant term c.
4. Click “Calculate”.
5. The calculator will display the two solutions (real or complex), or tell you if there are no real roots.

Formula Used:

The quadratic formula is:

$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$

Where:

• a, b, and c are the coefficients from the quadratic equation ax² + bx + c = 0.

• The part under the square root, b² - 4ac, is called the discriminant:

  • If it’s positive: Two real solutions.

  • If it’s zero: One real solution (a repeated root).

  • If it’s negative: Two complex solutions.

Example:

Solve the equation 2x² - 4x - 6 = 0

Here:

• a = 2

• b = -4

• c = -6

Plug into the formula:

$$x = \frac{-(-4) \pm \sqrt{(-4)^2 – 4(2)(-6)}}{2(2)} = \frac{4 \pm \sqrt{16 + 48}}{4} = \frac{4 \pm \sqrt{64}}{4}$$

$$$$$$x = \frac{4 \pm 8}{4}$$

So the solutions are:

• $x = \frac{4 + 8}{4} = 3$
  

• $x = \frac{4 – 8}{4} = -1$
  

Final Answer: x = 3 and x = -1