Answer
$\frac{\pi}{3}, \frac{5\pi}{3}$
Work Step by Step
Step 1. Rewrite the equation as $2cos^2(x)-1+3=5cos(x)$; we have $2cos^2(x)-5cos(x)+2=0$
Step 2. Let $u=cos(x)$; we have $2u^2-5u+2=0$ or $(2u-1)(u-2)=0$
Step 3. For $cos(x)=u=2$, there is no solution.
Step 4. For $cos(x)=u=\frac{1}{2}$, we have $x=\frac{\pi}{3}, \frac{5\pi}{3}$ over the interval of $[0,2\pi)$
