None at All

Try the root method on x^2 = -9. It asks for a number whose square is negative, and among real numbers there is none: squares are never negative. The board itself will refuse the move and tell you why. The equation simply has no real solution, and that is a finished, correct answer.

The formula meets the same wall more politely: x^2 + 2x + 5 = 0 has discriminant 4 - 20 = -16, and the root of a negative number stops the real-number story right there.

No real solutions is not failure; it is information. The parabola never touches the axis; the story problem has no answer in real quantities. Later mathematics builds numbers beyond the reals where these equations bloom, an account for another journey.