Answer
$\{-4,-3\}$
Work Step by Step
Step 1. Rearrange the equation as $\sqrt {3x+13}=x+5$
Step 2. Take the square on both sides to get
$3x+13=x^2+10x+25$ or $x^2+7x+12=0$
Step 3. Factor the equation to get $(x+3)(x+4)=0$ which gives $x=-4, -3$
Step 4. Check $x=-4$; we have $LHS=\sqrt {3(-4)+13}=1=RHS$
Step 5. Check $x=-3$; we have $LHS=\sqrt {3(-3)+13}=2=RHS$
Step 6. We conclude that the solutions are $x=-4$ and $x=-3$ or $\{-4,-3\}$