I don't know if the solution is accurate or not but here is the method.
I have used a couple of approximations and assumptions.
Assuming a > 0 and for x << a
we can rewrite the equation as
exp(a-x) = (x-c)/(b-x) ;
adding one two both sides :
1 + exp(a-x) = (b-c)/(b-x);
and...