I have no idea how to do this one:

Sqrt(3x+4) + Sqrt(x-3) = 5

I did guess and check and found that x = 4, but I want a more elegant solution. I did try squaring both sides and came up with

3x + 4 + x - 3 + 2Sqrt(3x^2 - 5x -12) = 25 but, long story short, that did not turn out right for me. Am i on the right track?