Three Kinds of Answers

The discriminant sits under the square root in the formula, and a square root behaves in three ways depending on the sign of what is under it. So, when a, b and c are real, the sign tells you what the answers look like before you solve anything.

Positive: the root is a real number and the ± gives two different real answers. ${x}^{2}-6x+5 = 0$ has discriminant 16, and its solutions are 1 and 5. Zero: the root is 0, so adding it and subtracting it give the same number. ${x}^{2}+2x+1 = 0$ has discriminant $4-4$, and its only solution, -1, is called a repeated solution.

Negative: the root of a negative number needs i, so both answers are complex. For ${x}^{2}+2x+5 = 0$ the discriminant is $4-20$, which is -16, and the formula gives $\frac{-2\pm\sqrt{-16}}{2}$: $x = -1+2i$ and $x = -1-2i$. The ± makes them conjugates, with the same real part and opposite imaginary parts. When a, b and c are real, complex solutions always come in such a pair.