None at All

The equation x^2 = -9 has no real solution. A positive number squared is positive, a negative number squared is positive, and zero squared is zero. So the square of a real number is never negative, and no real number has -9 as its square. The answer is that there is no real solution.

The discriminant tells you the same thing for any quadratic equation. For x^2 + 2x + 5 = 0, the discriminant is 2^2 - 4 × 1 × 5 = -16. It is negative, so the quadratic formula would ask for the square root of -16, and the equation has no real solutions.

When the discriminant is negative, the quadratic equation has no real solutions, and its graph never touches the x-axis. The final answer is then written as no real solutions. There are other numbers, called complex numbers, that can solve such equations, but they are not part of this section.