Answer
$\{-\frac{2}{9},2\}$
Work Step by Step
Step 1. Given the equation $\sqrt {2\sqrt {7x+2}}=\sqrt {3x+2}$
Step 2. Take square on both sides to get: $2\sqrt {7x+2}=3x+2$
Step 3. Take square on both sides again to get: $28x+8=9x^2+12x+4$ or $9x^2-16x-4=0$ which gives $x=-\frac{2}{9},2$
Step 4. Check answers in the original equation: both $\{-\frac{2}{9},2\}$ fit.
