Answer
$\color{blue}{\left\{-\frac{1}{2}, 5\right\}}$
Work Step by Step
The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Write the given equation in $ax^2+bx+c=0$ form to obtain:
$$2x^3-9c-5=0$$
The equation above has $a=2, b=-9, \text{ and } c= -5$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-5)}}{2(2)}\\\\
x&=\frac{9\pm \sqrt{81+40}}{4}\\\\
x&=\frac{9\pm \sqrt{121}}{4}\\\\
\end{align*}
Thus,
$x_1=\dfrac{9+11}{4}=\dfrac{20}{4}=5\\\\$
$x_2=\dfrac{9-11}{4}=\dfrac{-2}{4}=-\dfrac{1}{2}$
Therefore, the solution set is $\color{blue}{\left\{-\frac{1}{2}, 5\right\}}$.
