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Finding closed form roots for pseudo-trinomial

I have the below function: $$\pi(x) = \frac{s_0\cdot \left(1-\left(\frac{s_1}{s_1+x \cdot \lambda}\right)^{k}\right) \cdot r_1}{s_0\cdot \left(1-\left(\frac{s_1}{s_1+x \cdot \lambda}\right)^{k}\right) …
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Finding closed form roots for pseudo-trinomial

After spending some time on it, below is my proposed solution. We can undergo another change of variables to make it a trinomial: $t=\frac{1}{\sqrt{y}}$ and we obtain: \begin{align} A \cdot t^{k+1} + …
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