# Rearranging equation

• peterjaybee

#### peterjaybee

Hi, I have fitted a graph with a function of the form
$$y(x) = a + bx^{-2} + cx^{-4} + dx^{-6}$$

I now need to calculate x for a given y and have no idea how to go about rearranging this function.

I need to find x for a lot of y values, so I was hoping to write something in methematica, but I need to understand how to rearrange it before I can implement it in mathematica.

Hi, I have fitted a graph with a function of the form
$$y(x) = a + bx^{-2} + cx^{-4} + dx^{-6}$$

I now need to calculate x for a given y and have no idea how to go about rearranging this function.

I need to find x for a lot of y values, so I was hoping to write something in methematica, but I need to understand how to rearrange it before I can implement it in mathematica.

Numerical techniques can be used, but if you want to solve it algebraically, then you can try the substitution u=1/x2 and then use the usual cubic polynomial algebraic solution to solve for u.

There is a cubic solution cheat sheet at the end of this thread.