Answer
$\{0,3\}$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {3x}+1=\sqrt {5x+1}$
Step 2. Take square on both sides to get: $3x+2\sqrt {3x}+1=5x+1$ or $\sqrt {3x}=x$
Step 3. Take square on both sides again to get: $3x=x^2$ or $x^2-3x=0$ which gives $x=0,3$
Step 4. Check answers in the original equation: they both fit.