Find all solutions of given equation
2cosx-1=0

There are an infinite number of solutions, so I don't plan to list them all.
I'll list two of them, and then describe how to get all of the rest.

You said that      2cos(x) - 1  =  0

Add  1  to each side:     2cos(x) = 1

Divide each side by  2:    cos(x) = 1/2

The angles whose cosine is 1/2 are  60 degrees, 300 degrees,
and any multiple of 360 degrees added to either of those.