Find $W_1$ branch of Lambert $W$-function

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The given equation: $$\frac{8} {\ln(2)} \cdot \ln(x) = x.$$

Some algebra, and then we get the solutions:

$$x = e^{W_0(-\frac{\ln(2)} {8})}\approx 1.1 ,\;\; x = e^{W_{-1}(-\frac{\ln(2)} {8})} \approx 43.5593.$$

I found $W_{0}$ with Taylor series.

But there is addition real solution, $W_{-1}$.

How I find the $W_{-1}$?