8.035. $3 \sin ^{2} 2 x+7 \cos 2 x-3=0$.

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8.035. $3 \sin ^{2} 2 x+7 \cos 2 x-3=0$.
## Solution.

We have

$$
\begin{aligned}
& 3\left(1-\cos ^{2} 2 x\right)+7 \cos 2 x-3=0 \Leftrightarrow 3 \cos ^{2} 2 x-7 \cos 2 x=0 \\
& \cos 2 x(3 \cos 2 x-7)=0
\end{aligned}
$$

From this:

1) $\cos 2 x=0, \quad 2 x=\frac{\pi}{2}+\pi k, \quad x_{1}=\frac{\pi}{4}+\frac{\pi k}{2}=\frac{\pi}{4}(2 k+1), k \in Z$;
2) $3 \cos 2 x-7=0, \cos 2 x=\frac{7}{3}>1-\varnothing$.

Answer: $\quad x=\frac{\pi}{4}(2 k+1), \quad k \in Z$.