Answer
$\emptyset$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {x+3}=\sqrt {3x+10}+1$
Step 2. Take square on both sides to get $x+3=3x+10+2\sqrt {3x+10}+1\longrightarrow 2\sqrt {3x+10}=-2x-8 \longrightarrow \sqrt {3x+10}=-x-4$
Step 3. Take square on both sides to get $3x+10=x^2+8x+16\longrightarrow x^2+5x+6=0$
Step 4. Factor the equation to get $(x+3)(x+2)=0$, thus $x=-3$ and $x=-2$
Step 5. Check the answer with the original equation and none fits, thus the solution set is $\emptyset$
