Hey man that formula is definitely right, for your example I got x = 1/6 as well.

0 = 30x + (0.2)(1-x)(50) + (1-x)(0.8)(-20)
0 = 30x + (1-x)(10-16)
0 = 30x - 6 + 6x
x = 1/6

Looking over your stuff this stands out.

Villain calls we lose = (1-x)(0.5582)(90)
Should be -90 in the brackets, try it again with that.