2x^3 +0.41*x^2 -1.4*10^(-8) = 0

Solving of cubic equation gives for x = 0.0002 mol/l means 92,2 mg/l PbI2

It's a deviation of 8%

This is wrong, and it is obvious even without checking the exact solution of the cubic equation. Solubility calculated assuming concentration of Pb

^{2+} didn't change is about four orders of magnitude lower than the concentration of Pb

^{2+} already present, so the assumption is perfectly valid. No way to get substantially different result with exact calculations.

And then, Wolfram Alpha to the rescue. 0.00018 again.

(Then, there is the mistake pointed out by mjc123, but it doesn't change the fact both solutions have to be almost identical.)