Find roots of polynomial $$ p(x) = \frac{393}{100}+6x-300 $$

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

$$ \begin{aligned}x &= \frac{ 9869 }{ 200 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.

$$ \begin{aligned} \frac{393}{100}+6x-300 & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 393+600x-30000 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ \color{blue}{393} +600x \color{blue}{-30000} = 600x \color{blue}{-29607} $$

Step 3:

$$ \begin{aligned} 600x-29607 & = 0 \\[1 em] 600 \cdot x & = 29607 \\[1 em] x & = \frac{ 29607 }{ 600 } \\[1 em] x & = \frac{ 29607 : 3 }{ 600 : 3} \\[1 em] x & = \frac{ 9869 }{ 200 } \end{aligned} $$

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