Answer
$x=\frac{2}{3},-1\pm\sqrt 2$
Work Step by Step
Step 1. For $3x^3+4x^2-7x+2=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm\frac{1}{3},\pm\frac{2}{3}$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=\frac{2}{3}$.
Step 3. Use the quotient to find other zeros: $3x^2+6x-3=0 \Longrightarrow x^2+2x-1=0 \Longrightarrow x=\frac{-2\pm\sqrt {4-4(-1)}}{2}=-1\pm\sqrt 2$
