That is the quadratic formula. People use that to solve quadratic equations, the standard form ax^2 + bx + c = 0. So, for instance, if you have:
2x^2 + 10x + 12 = 0
You would have a = 2, b = 10, and c = 12. You would plug those values into the quadratic formula to determine what x is, here, x = -2 and x = -3.
This formula works everytime. Unlike factoring, which only works if you can factor it. This can even give you any imaginary solutions, as well.