John Henry

I want, if possible, to rearrange this equation in terms of C:

A = B * (1+C)^D - E * ((1+C)^D-1) / C

I've got a feeling it can't be done (I should really be able to tell, with an A-level in maths and an MPhys) so at the moment I'm evaluating it with numerical methods, but that's slow. I was just wondering if there were any mathematical geniuses out there who might know a way to do it, or could at least confirm my fears.

I had wondered about using a substitution of (1+C)^D=F, giving

C=F^(1/D)-1

and

A=BF - EF/C - E

then multiplying through by F and rearranging to get a quadratic, then solving that using what my maths teacher used to call "The Equation", giving:

F=(E/C-A)/(E/C+E)

then rearranging, subbing C back in and multiplying through by C, leaving us with:

(E+BC)(C+C^2)^D-AC+E=0

And that's as far as I can go. Don't know if this is solvable from here. My gf just suggested that integration might help (0 to D dC), but I can't work it out. Also, I don't know if I've worked it out properly so far as my algebra is often dodgy.

Thanks in advance for any help you can provide, people.

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