Answer
$\{\frac{4}{3}, 2\}$
Work Step by Step
Step 1. Given the equation $\sqrt[3] {3x^2-9x+8}=\sqrt[3] {x}$
Step 2. Raise 3rd power on both sides to get: $3x^2-9x+8=x$ or $3x^2-10x+8=0$ which gives $x=\frac{4}{3}, 2$
Step 3. Check answers in the original equation: both $\{\frac{4}{3}, 2\}$ fit.
