Question

how would you solve a quadratic function

Answer 1

Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring.

Answer 2

There are numerous methods available to you, including, but not limited to, 

completing the square
factoring
quadratic formula
graphing 

If factoring appears easy, I factor.  Otherwise I'd likely choose either completing the square or the quadratic formula.