MOSFET operating point in linear mode
Where you stopped showing your work is where you went wrong. Solving the quadratic equation, I didn't get the same results.
Here's Wolfram Alpha's interpretation.
The roots they find are +0.04V and +4.6V. With these numbers, it should be more obvious which one is incorrect as one of them violates the &quot;Not in saturation&quot; conclusion you found earlier.