The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= \dfrac{ 2 }{ 3 } \end{aligned} $$Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} x-\frac{2}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 3x-2 & = 0 \end{aligned} $$Step 2:
$$ \begin{aligned} 3x-2 & = 0 \\[1 em] 3 \cdot x & = 2 \\[1 em] x & = \frac{ 2 }{ 3 } \end{aligned} $$