Find roots of polynomial $$ p(x) = 12x-\frac{5}{3}x-\frac{1}{2} $$

The root of polynomial $ p(x) $ is:

$$ \begin{aligned}x &= \frac{ 3 }{ 62 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 6 } $.

$$ \begin{aligned} 12x-\frac{5}{3}x-\frac{1}{2} & = 0 ~~~ / \cdot \color{blue}{ 6 } \\[1 em] 72x-10x-3 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ \color{blue}{72x} \color{blue}{-10x} -3 = \color{blue}{62x} -3 $$

Step 3:

$$ \begin{aligned} 62x-3 & = 0 \\[1 em] 62 \cdot x & = 3 \\[1 em] x & = \frac{ 3 }{ 62 } \end{aligned} $$

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