Answer
$\frac{-1-2\sqrt 2}{3},\frac{-1+2\sqrt 2}{3}$
Work Step by Step
Step 1. Use the square root property, take square root on both sides, we have $(3x+1)^2=8\longrightarrow 3x+1=\pm\sqrt 8=\pm2\sqrt 2$
Step 2. Thus the solutions are $x=\frac{-1-2\sqrt 2}{3}$ and $x=\frac{-1+2\sqrt 2}{3}$
