Answer
$8$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {5x-15}=\sqrt {x+1}+2$
Step 2. Take square on both sides to get $5x-15=x+1+4\sqrt {x+1}+4\longrightarrow 4\sqrt {x+1}=4x-20 \longrightarrow \sqrt {x+1}=x-5$
Step 3. Take square on both sides to get $x+1=x^2-10x+25\longrightarrow x^2-11x+24=0$
Step 4. Factor the equation to get $(x-3)(x-8)=0$, thus $x=3$ and $x=8$
Step 5. Check the answers with the original equation and only $x=8$ fits