Answer
$\{8\}$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {2x}+2=\sqrt {3x+12}$
Step 2. Take square on both sides to get: $2x+4\sqrt {2x}+4=3x+12$ or $4\sqrt {2x}=x+8$
Step 3. Take square on both sides again to get: $32x=x^2+16x+64$ or $x^2-16x+64=0$ which gives $x=8$
Step 4. Check answer in the original equation: it fits.