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

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SUMMARY

The discussion centers on solving the inverse third order equation represented as y = y0 + (a/x) + (b/x2) + (c/x3). The user seeks to isolate X while having known values for a, b, c, and y0. The solution involves multiplying the equation by x3 to convert it into a cubic polynomial, which can then be solved using Cardano's method for finding the roots of cubic equations.

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cooka111
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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[tex]_{0}[/tex]+[tex]\frac{a}{x}[/tex]+[tex]\frac{b}{x^{2}}[/tex]+[tex]\frac{c}{x^{3}}[/tex]

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