What is the solution for an inverse third order equation when solving for X?

[cooka111]

I have a question about solving a formula.

I have a set of data which I have fit to an inverse third order equation, if I swap the axes (use X as Y and vise versa), R2 suffers dramatically but I would like to calculate both Y and X values independantly. I am wondering what the solution for the following equation is when cast to calculate X. My algebra is a little rusty and I am not sure where to start.

y = y$$_{0}$$+$$\frac{a}{x}$$+$$\frac{b}{x^{2}}$$+$$\frac{c}{x^{3}}$$

Assuming I have values for a,b,c, and yo, how do I solve this for x?

 

[Pere Callahan]

Welcome to PF.

Multiply the equation by x^3 and you get a polynomial of degree three, whose roots are given by http://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method".