Is there an approach to solve the following radical equation in $x$?
$(P - 1)x = QR\left( Q + \sigma \sqrt{Q^2 + x} \right)\left( R + sign(P-1) \sigma \sqrt{R^2 + x} \right)$
We know $x\in (0,1)$. We also have $P, Q, R > 0$ and $\sigma \in \{-1,+1\}$.