Answer
$z= -9.35, z= 1.15$
Work Step by Step
Use the quadratic formula. $$
\begin{aligned}
& (z+9)(5 z-4)=18 \\
& (z+9) \cdot 5 z-4(z+9)=18 \\
& 5 z^2+45 z-4 z-36=18 \\
& 5 z^2+41 z-36-18=0 \\
& 5 z^2+41 z-54=0.
\end{aligned}
$$Set $$
\begin{aligned}
a & =5 \\
b& =41\\
c & =-54
\end{aligned}
$$ $$
\begin{aligned}
z&= \frac{-b\pm \sqrt{b^2-4ac}}{2a}\\
z& =\frac{-(41) \pm \sqrt{(41)^2-4 \cdot 5 \cdot (-54)}}{2 \cdot 5}\\
& =\frac{-41 \pm \sqrt{2761}}{10}\\
\end{aligned}
$$ This gives $$
\begin{aligned}
z & =\frac{-41-\sqrt{2761}}{10}\\
& \approx -9.35\\
z & =\frac{-41+\sqrt{2761}}{10} \\
& \approx1.15
\end{aligned}
$$ We got:
$$z= -9.35 \text{ or } z= 1.15$$ Define the following function and plot it. We see that the zeros are where they should be.
$$
f(z) =5 z^2+41 z-54=0.
$$
