#### Answer

$x = 0.692$
$x = 2.082$

#### Work Step by Step

$3cos~\frac{x}{2}+\sqrt{x}-2 = -\frac{x}{2}+2$
We can graph the two equations $~~y = 3cos~\frac{x}{2}+\sqrt{x}-2 ~~$ and $~~y = -\frac{x}{2}+2~~$ to find the points of intersection.
The blue graph is $~~y = -\frac{x}{2}+2~~$
The red graph is $~~y = 3cos~\frac{x}{2}+\sqrt{x}-2 ~~$
On the interval $[0,2\pi]$, we can see that the points of intersection occur when $~~x = 0.692~~$ and $~~x = 2.082$
The solution over the given interval is:
$x = 0.692$
$x = 2.082$