A method for solving quadratic equations involves the quadratic equation.  An equation of the form:

ax² + bx + c = 0

where a ≠ 0

has the following solution(s) for x: 

The value of the terms under the radical, which is referred to as the discriminant, is represented by the Greek letter delta as follows:

Δ = b² − 4ac

1) For Δ = b² − 4ac > 0: 

Equation has two real and unequal roots (Reference Example #1 below)

2) For Δ = b² − 4ac = 0: 

Equation has a single root (double root) (Reference Example #2 below)

3) For Δ = b² − 4ac < 0:

Equation has no real roots; its roots are two complex numbers that are complex conjugates of each other (Reference Example #3 below)