So,
Given:

We want to find the value of x when f(x) = -4.
For this, we could replace:

Now, let's solve this quadratic equation:
We could apply the quadratic formula as follows;
Given a quadratic equation of the form:

The solutions of this equation can be found using the following formula:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/rxvf73usjbbwyik14knxdemoz21vfz2ufc.png)
If we replace the values of our equation, these are:
a=8
b=18
c=9
Thus,
![\begin{gathered} x=\frac{-18\pm\sqrt[]{18^2-4(8)(9)}}{2(8)} \\ \\ x=\frac{-18\pm\sqrt[]{36}}{16}\to\begin{cases}x_1=(-18+6)/(16)=(-12)/(16)=-(3)/(4) \\ x_2=(-18-6)/(16)=(-24)/(16)=-(3)/(2)\end{cases} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ruk9tzjs38vyi9rktgbxfhndnpmvdbkse1.png)
Therefore, the values of x are -3/2 and -3/4