Answer
$1.9106, 4.3726$
Work Step by Step
Step 1. Let $u=cos(x)$; we can rewrite the equation as $3u^2-8u-3=(3u+1)(u-3)=0$ which gives $u=3$ and $u=-\frac{1}{3}$
Step 2. For $cos(x)=u=3$, there is no solution.
Step 3. For $cos(x)=u=-\frac{1}{3}$, we can find the reference angle as $x_0=cos^{-1}(\frac{1}{3})\approx1.2310$; thus we get all x-values in $[0,2\pi)$ as $x=\pi\pm x_0$ or $x\approx1.9106, 4.3726$
