The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= -\dfrac{ 4 }{ 7 } \end{aligned} $$Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 200 } $.
$$ \begin{aligned} \frac{7}{200}x+\frac{1}{50} & = 0 ~~~ / \cdot \color{blue}{ 200 } \\[1 em] 7x+4 & = 0 \end{aligned} $$Step 2:
$$ \begin{aligned} 7x+4 & = 0 \\[1 em] 7 \cdot x & = -4 \\[1 em] x & = - \frac{ 4 }{ 7 } \end{aligned} $$