The discriminant is b2−4ac, the part under the square root in the quadratic formula. It tells you how many real solutions exist.
If b2−4ac>0, you have two distinct solutions. If b2−4ac=0, you have one solution (repeated root). If b2−4ac<0, you have no real solutions (only complex).
Before computing the square root, check the discriminant. If it's negative and you only need real answers, you can skip the calculation.