Answer
$4$.
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {3x+4}=2x-4$
Step 2. Take square on both sides to get $3x+4=(2x-4)^2\longrightarrow 3x+4=4x^2-16x+16$
Step 3. Rewrite the equation as $4x^2-19x+12=0$
Step 4. Factor the equation to get $(4x-3)(x-4)=0$, we have $x=\frac{3}{4}$ and $x=4$
Step 5. Check the above answers and we find only $x=4$ fits the original equation, thus the solution is $x=4$.
