Using the quadratic formula and the discriminant:
When you are faced with the equation y = ax^2 + bx + c, and it can neither be simplified or factored further, use the quadratic formula:
I cannot stress the importance of this formula enough, you must commit it to memory by any means necessary, I recommend tattooing it to your body, but that's only my opinion.
Now that you've memorized the formula either by tattoo or another means, we can discuss the discriminant. The discriminant is the expression found under the radical, or b^2 - 4ac; if the expression, when solved, is positive, then there are two real solutions to the function. If the discriminant is negative, there are no real solutions, and if the discriminant is zero, then there is one real solution to the function.