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cooka111
Apr21-08, 10:56 AM
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
Apr21-08, 06:05 PM
Welcome to PF.

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