The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= 1 \end{aligned} $$Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.
$$ \begin{aligned} \frac{1}{8}x-\frac{1}{8} & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] x-1 & = 0 \end{aligned} $$Step 2:
$$ \begin{aligned} x-1 & = 0 \\[1 em] x & = 1 \end{aligned} $$