Ok, so if anyone reads these things just for fun, here is the correct way to solve the problem.
Start out with the equation & then make your ICE table
CH3CO2H + H2O -> H3O+ + CH3CO2
I .1 0 .1
C -x x x
E .1-x x .1+x
So your equation then becomes
(x(.1+x))/(.1-x)=1.85 x 10^-5
Then its basic math to solve for x which gives the correct answer of 1.85 x 10^-5 M H+.