In elementary algebra , the quadratic formula is the solution of the quadratic equation . There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring , completing the square , or graphing . Using the quadratic formula is often the most convenient way.
where x represents an unknown, and a , b , and c represent known numbers such that a is not equal to 0 . If a = 0 , then the equation is linear , not quadratic. The numbers a , b , and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient , the linear coefficient and the constant or free term . 
The blue part ( b 2 - 4ac ) is called the "discriminant", because it can "discriminate" between the possible types of answer. If it is positive, you will get two real solutions, if it is zero you get just ONE solution, and if it is negative you get complex solutions.