Quadratic Formula Calculator

Online Quadratic Formaula calculator, compute the values of each given relative value

The Quadratic Formula is a powerful tool used to solve quadratic equations that may not be factorable. This formula is applicable to any quadratic equation of the form ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Quadratic Formula Calculator
Quadratic Equation:
Ax2 + Bx + C = 0
A =
B =
C =
X1 =
X2 =

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Interesting Facts

  • The Quadratic Formula is also known as the "Quadratic Equation Formula" or "Completing the Square".
  • The formula is attributed to the ancient Babylonians, who used it to solve complex algebraic problems.
  • The Quadratic Formula can be derived from the process of "completing the square", which involves adding a constant term to a quadratic expression to create a perfect square trinomial.

The Formula

The Quadratic Formula is:

x = (-b ± √(b2 - 4ac)) / 2a

Where x is the variable being solved for, and a, b, and c are the coefficients of the quadratic equation. The ± sign indicates that there are two solutions to the equation, one with a plus sign and one with a minus sign.


Let's say you have a quadratic equation: 2x2 + 5x - 3 = 0

To solve for x using the Quadratic Formula, first identify the values of a, b, and c:

  • a = 2
  • b = 5
  • c = -3

Then plug these values into the Quadratic Formula:

x = (-5 ± √(52 - 4(2)(-3))) / 2(2)

Simplifying the formula gives two solutions:

  • x = (-5 + √49) / 4 = 1/2 or -3
  • x = (-5 - √49) / 4 = -3 or 1/2

Therefore, the solutions to the quadratic equation 2x2 + 5x - 3 = 0 are x = 1/2 and x = -3.

Real-Life Applications

The Quadratic Formula has many real-life applications, such as:

  • Calculating projectile motion in physics
  • Optimizing profits in business
  • Modeling population growth in biology
  • Designing bridges and buildings in engineering

By understanding how to use the Quadratic Formula Calculator, you can solve complex quadratic equations and apply them to a variety of real-world situations.