cos(a) = cos(b)
means (taking inverse cos)
a = +/-b + 360k
where k is an integer. Which answer do you want? Remember cos is symmetric about 0 degrees.
In your working, you've made a mistake not putting (x-20) in brackets when you take inverse cos. Hence the sign of 20 is wrong. Also, the 90 in the right as you can't take the inverse cos of two terms on the left as well.