Polynomial $ p(x) $ has no zeros.
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} \frac{8}{3}-1-\frac{2}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 8-3-2 & = 0 \end{aligned} $$Step 2:
Combine like terms:
$$ \color{blue}{8} \color{red}{-3} \color{red}{-2} = \color{red}{3} $$Step 3:
Equation $ 3 = 0 $ has no solutions.