The quadratic equation (also known as the second degree equation) is second degree polynomial with the form ax² + bx + c equals to zero.

Divide the equation by the first term or coefficient of the original equation "a"

Complete the square with

By adding and substracting

it can be written as

Solve the equation taking advantage of can be easily isolated.

The value of x in the box is known as the general formula for the quadratic equation

The fundamental theorem of the algebra guarantees that a second degree polynomial has 2 roots. If you check the formula there are 2 signs, "+" and "-" that are just the ones that generate both solutions for the equation.

If discriminant greater than zero the equation has 2 real and different solutions

If discriminant equal to zero both solutions are equal

If discriminant less than zero the roots are complex conjugate