So I have the following equation from the 2002 paper "A Rapid Hierarchical Rendering Technique for Translucent Materials" http://graphics.ucsd.edu/~henrik/papers/fast_bssrdf/fast_bssrdf.pdf
Here is an equation from that paper where they suggest finding the value alpha_prime by inverting the equation and inputing a desired value for Rd.
However, I'm really not at all sure how to invert this equation. As you can see in the picture, the paper recommends using a "secant root finder". I tried looking up what a secant root finder is, but I'm having trouble understanding what it is, how it is used and how it can be applied to this equation.
I've also tried plugging this equation into Wolfram Alpha and asking it to invert it for me but it didn't work.
So I was wondering if someone here on this site could help me invert the equation.
I suggest change variable $\alpha'=1-\frac{t^2}{3}$, approximate exponent by its Tailor series, substitute and then find roots in appropriate interval using mathlab.