The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\frac{ 1 }{ 20 }+\frac{\sqrt{ 1191 }}{ 60 }i\\[1 em]x_2 &= -\frac{ 1 }{ 20 }- \frac{\sqrt{ 1191 }}{ 60 }i \end{aligned} $$Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.
$$ \begin{aligned} 3x^2+\frac{3}{10}x+1 & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] 30x^2+3x+10 & = 0 \end{aligned} $$Step 2:
The solutions of $ 30x^2+3x+10 = 0 $ are: $ x = -\dfrac{ 1 }{ 20 }+\dfrac{\sqrt{ 1191 }}{ 60 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 20 }-\dfrac{\sqrt{ 1191 }}{ 60 }i$.
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