Find roots of polynomial $$ p(x) = \frac{13}{5}x^2-3x-9 $$

The roots of polynomial $ p(x) $ are:

$$ \begin{aligned}x_1 &= 2.5248\\[1 em]x_2 &= -1.371 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 5 } $.

$$ \begin{aligned} \frac{13}{5}x^2-3x-9 & = 0 ~~~ / \cdot \color{blue}{ 5 } \\[1 em] 13x^2-15x-45 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 13x^2-15x-45 = 0 $ are: $ x = \dfrac{ 15 }{ 26 }-\dfrac{ 3 \sqrt{ 285}}{ 26 } ~ \text{and} ~ x = \dfrac{ 15 }{ 26 }+\dfrac{ 3 \sqrt{ 285}}{ 26 }$.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.

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