$\displaystyle 0=-\frac{\sqrt{x+2}(x-7)}{2}+12$
The method here is the same as before. If we multiply by 2 throughout:
Again $\displaystyle x > -2 $
$\displaystyle 0 = -(x-7)\sqrt{x+2} + 24$
$\displaystyle (x-7)\sqrt{x+2} = 24$
square both sides
$\displaystyle (x-7)^2(\sqrt{x+2})^2 = 24^2$
Simplify and solve for x. Remember to check for extraneous solutions