Maximizing Energy Density: How to Find the Optimal Frequency?

[morbidwork]

Homework Statement

u(f, T) = (8 pi h f^3)/(c^3 (e^(h f/ k T) - 1))
find an equation for the frequency, fmax, at which the energy density, u, is a maximum.

Homework Equations

C,h,pi, and k are constants.

The Attempt at a Solution

I took the derivative and set the equation equal to 0. My problem is I end up with a non-analytical equation. Instead I end up with the transcendental equation:

3(e^x - 1) - x e^x = 0 which I am not sure how to solve I know I must use Lambert's Product Law but I am unsure of how the W function works.edit
as well x = (h f)/(k T)

 

[malawi_glenn]

Solve it nummerically instead, or iterate.