The fastest way is with factoring.
x2 + 5x + 6 = 0
(x+2)(x+3) = 0
Set each factor equal to zero.
x + 2 = 0 and x + 3 = 0
x = -2 and x = -3
You can also use the quadratic formula.
\(ax^{2}+bx+c=0 \\ x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\ a=1, b=5, c=6 \\ x = {-5 \pm \sqrt{5^2-4(1)(6)} \over 2(1)} \\ x = {-5 \pm \sqrt{1} \over 2} \\ x = \frac{-5+1}{2} \text{ and } x = \frac{-5-1}{2} \\ x=-2 \text{ and } x=-3\)
A third method is called completing the square, here's an explanation of that method:
https://www.youtube.com/watch?v=bNQY0z76M5A
