8.155. $\frac{2 \cos (\pi+x)-5 \cos \left(\frac{3}{2} \pi-x\right)}{\cos \left(\frac{3}{2} \pi+x\right)-\cos (\pi-x)}=\frac{3}{2}$.
## Solution.

Domain of definition: $\sin x+\cos x \neq 0$.

Using reduction formulas

$$
\begin{aligned}
& \frac{-2 \cos x+5 \sin x}{\sin x+\cos x}-\frac{3}{2}=0 \Rightarrow 7 \sin x-7 \cos x=0 \Leftrightarrow \operatorname{tg} x=1 \\
& x=\frac{\pi}{4}+\pi k=\frac{\pi}{4}(4 k+1), \quad k \in Z
\end{aligned}
$$

Answer: $\quad x=\frac{\pi}{4}(4 k+1), k \in Z$.