Quadratic Equation Calculator

Use this handy tool to solve any quadratic equations given in standard form.

  • First, enter the coefficients a, b, and c (a≠0) of the quadratic equation ax2+bx+c=0. Make sure you have entered the correct number of digits using our sig fig calculator.
  • Next, click on the "Calculate" button and the solution will be displayed.

Our quadratic equation calculator can solve quadratic equations with real or complex roots. It will calculate the discriminant D=(b2-4ac) and determine whether it is equal to, greater than, or less than zero.

If the discriminant is equal to zero, the equation has one real root (called a double root); if it is greater than zero, the equation has two distinct real roots; if it is less than zero, the equation has two complex roots.

Quadratic Formula Calculator

x2 + x + =0

Quadratic Formula

The calculator uses the following formula:

x = (-b ± √D) / 2a, where D = b2 - 4ac

This formula calculates the solution of quadratic equations (ax2+bx+c=0) where x is unknown, a is the quadratic coefficient (a ≠ 0), b is the linear coefficient and c represents the equation's constant. The letters a, b and c are known numbers and are the quadratic equation's coefficients.

Quadratic Equation Example

For example, let's take the equation 2x2-6x+3=0, where a = 2, b = -6, and c = 3.

D = b2 - 4ac = (-6)2-4·2·3 = 36-24 = 12

Since the discriminant is greater than zero, the equation has two real roots. These roots are found using the quadratic formula:

x(1,2) = (-b ± √D) / 2a

x1 = (-b + √D) / 2a = (-(-6)+3.46) / 2·2 = 9.46 / 4 = 2.37 (rounded to 3 sig figs)

x2 = (-b - √D) / 2a = (-(-6)-3.46) / 2·2 = 2.54 / 4 = 0.63 (rounded to 3 sig figs)

The solution is x1=2.37, x2=0.63

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