We have:
$2\sin^2 x - 3 = 3\cos x \Rightarrow 2(1 - \cos^2 x) - 3 = 3\cos x \Rightarrow 2\cos^2 x + 3\cos x - 1 = 0$
Now, we have a quadratic equation in $\cos x$. We can solve for $\cos x$ using the quadratic formula:
$\cos x = \frac{-3 \pm \sqrt{(-3)^2 -
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