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

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

$$ \begin{aligned}x_1 &= 0.9059\\[1 em]x_2 &= -1.6559 \end{aligned} $$

Step 1:

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

$$ \begin{aligned} -2x^2-\frac{3}{2}x+3 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] -4x^2-3x+6 & = 0 \end{aligned} $$

Step 2:

The solutions of $ -4x^2-3x+6 = 0 $ are: $ x = -\dfrac{ 3 }{ 8 }-\dfrac{\sqrt{ 105 }}{ 8 } ~ \text{and} ~ x = -\dfrac{ 3 }{ 8 }+\dfrac{\sqrt{ 105 }}{ 8 }$.

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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