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

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

$$ \begin{aligned}k &= \frac{ 24 }{ 11 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.

$$ \begin{aligned} \frac{5}{2}k+3k-12 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 5k+6k-24 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ \color{blue}{5k} + \color{blue}{6k} -24 = \color{blue}{11k} -24 $$

Step 3:

$$ \begin{aligned} 11k-24 & = 0 \\[1 em] 11 \cdot k & = 24 \\[1 em] k & = \frac{ 24 }{ 11 } \end{aligned} $$

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