Are you expecting "a", "b", and "c" to be purely positive reals? If not then what meaning do you want to give to raising those values to the floating point power 1.75 ?
If you substitute the definition for c in to f(1) and f(2) you can reduce this to two equations in two variables. If you solve the parts for a in terms of b, and subtract the two and solve for 0, you find you are working with balancing the roots of a 32 degree polynomial against the roots of a 16 degree polynomial (I think it is). I am not convinced at the moment that any real roots exist.
I do not see how you can justify having some constants to 3 decimal places, some to 5, some to 2, and some of them to only 1 decimal place. The 32 degree polynomial needed to solve the expression becomes more or less numeric trash under those conditions.
