The equation is:
cotg(X) = (sqrt(3)*cos(50º) + sin(50º))*(1-2*sqrt(3)*cos(50º)+2*sin(50º)) /
(sqrt(3)*sin(50º) - cos(50º))
Using a calculator, I find X = 50º.
How to develop the equation to find the solution?
Doing what you propose with the calculator we arrive to 50 degrees.
So, if X = 50, it would be possible to "develop" or simplify the trigonometric expression on the second member of the equation to arrive to cotg(50).
Don't you think so, considering that in the expression we have only trigonometric functions of the same angle?