Quadratic Equation Calculator

Use our handy quadratic equation calculator to solve all quadratic problems.

  • First, enter the coefficients a, b, c (a≠0) of the quadratic equation ax2+bx+c=0.
  • Next, click on "Calculate" and the solution will be displayed.

Quadratic equations of all kinds, with real or complex roots, can be solved using the quadratic equation calculator. This useful tool will ascertain the discriminant D=(b2-4ac) and if it is equal to, greater than or less than zero.

When the discriminant is equal to zero, there is one real root in the equation; when it is greater than zero, there are two real roots; and when it is less than zero, there are two complex roots in the equation.

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

Let's take the example of 2x2-6x+3=0, where a represents 2, b represents -6 and c represents 3 and apply the quadratic formula to this equation.

In this instance, the quadratic equation's coefficients are as follows: a=2, b=-6, c=3

The determinant is ascertained in the following way: D = b2 - 4ac = (-6)2-4·2·3 = 36-24 = 12

Furthermore, as the discriminant is greater than zero, the equation has two real roots.

These two roots are found using the quadratic formula, as illustrated below:

x(1,2) = (-b ± √D) / 2a

x1 = (-b + √D) / 2a = (-(-6)+3.46) / 2·2 = 9.46 / 4 = 2.37

x2 = (-b - √D) / 2a = (-(-6)-3.46) / 2·2 = 2.54 / 4 = 0.63

Solution: x1=2.37, x2=0.63

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