The quadratic formula calculator is an online calculator to solve a standard quadratic equation using the Quadratic Formula, which is -

After solving the quadratic equation using a quadratic formula calculator, we get two values:

These two values of x, x₁ and x₂, which are calculated from Quadratic Formula Calculator, are also known as roots of quadratic equation.

Hence, Quadratic Formula Calculator calculates roots of a Quadratic equation

◾ If b² – 4ac > 0, then √b2 − 4ac  is real; in this case, Quadratic formula calculator gives us two real and distinct roots.

◾ If b² – 4ac = 0, then √b2 − 4ac  is zero; in this case, Quadratic formula calculator gives us real and equal roots.

◾ If b² – 4ac < 0, then √b2 − 4ac  is imaginary number; in this case, Quadratic formula calculator gives us imaginary roots.

◾ If b² – 4ac is a perfect square, then √b2 − 4ac  is a rational number; in this case, Quadratic formula calculator gives us rational roots, else Quadratic formula calculator gives us irrational roots

Step 1 - To use the Quadratic formula calculator, we have to convert the Quadratic Equation to be calculated into Standard Form of Quadratic Equation, ax² + bx + c = 0

For example, let' suppose, we have to solve a quadratic equation which is in the form, x² - 9x = -20. So in this case, we will convert the quadratic equation into Standard Form of Quadratic Equation, ax² + bx +c = 0

Hence, x² - 9x = -20 in standard form would be x² - 9x + 20 = 0

Step 2 - Now, we have to compare the derived quadratic equation in standard form which is x² - 9x + 20 = 0 with Standard Form of Quadratic Equation, ax² + bx +c = 0 and find the value of a, b and c.

For example, comparing x² - 9x + 20 = 0 with ax² + bx + c = 0, we get

a = 1,
b = -9,
c = 20

Step 3 - Once we have derived the value of coefficients a, b and c, then all we need is to insert these values in the quadratic formula, which is