The quadratic formula, shown below, is used to solve the roots of a quadratic equation.
Picture credit:
Fig.1
http://wwwchem.tamu.edu/class/fyp/mathrev/mr-quadr.html
There will always be two solutions for x. These may be real, identical or imaginary depending on the relationship between b^2 and 4ac.
If b^2 = 4ac, then there are two real, identical solutions.

If b^2 < 4ac, then there are two imaginary solutions.

If b^2 > 4ac, then there are two real, distinct solutions.
Quadratic
Equation
Fig. 1
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