Find roots of polynomial $$ p(x) = 5x^2+\frac{17}{5}x-22 $$

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

$$ \begin{aligned}x_1 &= 1.785\\[1 em]x_2 &= -2.465 \end{aligned} $$

Step 1:

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

$$ \begin{aligned} 5x^2+\frac{17}{5}x-22 & = 0 ~~~ / \cdot \color{blue}{ 5 } \\[1 em] 25x^2+17x-110 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 25x^2+17x-110 = 0 $ are: $ x = -\dfrac{ 17 }{ 50 }-\dfrac{\sqrt{ 11289 }}{ 50 } ~ \text{and} ~ x = -\dfrac{ 17 }{ 50 }+\dfrac{\sqrt{ 11289 }}{ 50 }$.

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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