Question
Find roots of polynomial $$ p(x) = -\frac{9}{2}x^2+48x-72 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 8.861\\[1 em]x_2 &= 1.8057 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} -\frac{9}{2}x^2+48x-72 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] -9x^2+96x-144 & = 0 \end{aligned} $$Step 2:
The solutions of $ -9x^2+96x-144 = 0 $ are: $ x = \dfrac{ 16 }{ 3 }-\dfrac{ 4 \sqrt{ 7}}{ 3 } ~ \text{and} ~ x = \dfrac{ 16 }{ 3 }+\dfrac{ 4 \sqrt{ 7}}{ 3 }$.
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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