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I am currently using the Callendar-Van Dusen Equation to solve for R(Resistance) when I input T(Temperature, in °C).

$$R(T) = R(0)(1 + AT + BT^2 + (T-100)CT^3)$$

I want to invert this equation so I can enter in R and get out T. I'm not very good at math, so this problem is pretty challenging for me. Any suggestions on how to solve it?

In my instance I'm using the following for $A,B$ and $C$.

$$\begin{array}{rl} A &= 3.9888*10^{-3}\\ B &= -5.915*10^{-7}\\ C &= -3.85 *10^{-12}\\ \end{array} $$

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  • $\begingroup$ It's a quartic equation with all coefficients nonzero. A closed form exists but it is a horrible mess that isn't worth dealing with. You're best off solving the problem numerically. For example if you have Matlab then this can be easily done using the "roots" function. Or for just one problem you could do it with Wolfram Alpha or similar websites. Note that you will need to be careful to pick the correct root, though there's a decent chance that there's only one positive root anyway. $\endgroup$ – Ian Mar 1 at 15:33

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