Find the values of x: $- 2 (1 - \cos x) = \frac x2$?

Question

How to find $x$?

The issue I have here is that $x$ is there even on the RHS.

If you could help it would be really nice as I have a test tomorrow.

Answer 1

Write the equation as $1+\frac x 4= cosx$ and draw the graph $y=1+\frac x 4$ and $y= cosx$, on the same figure you get three point of intersection. The values of $x$ are at the point of intersection of these two curve where one is zero and another two you have to find numerically or a given range.

Answer 2

Answering this as an answer since I don't have enough reputation to comment:

What is the solution of cos(x)=x? is similar to this question, and as the majority of answers point out, there is no solution in terms of standard functions, however you can prove it has solutions using IVT.