__http://i.imgur.com/5vLpo93.jpg__

One solution that was the most promising one was considering a triangle of slope m=1/Rs, height Idmax=(Vdd-Vds)/(Rs+Rd) and side of Vgs-Vth. Pic here of the math (triangle in red for better understanding)...

__http://i.imgur.com/kJXtH3B.jpg__

It gives complex Rs.

I have tried

**EVERYTHING**. I took derivatives of gm with respect to Rs, Id and whatever combination of the formulas above. I also tried combining formulas and see what comes out. For example, I put Id from the first formula written (the one with Idss and Vp, replacing Vgs with Vth-Id*Rs) equal to (Vdd-Vds)/(Rs+Rd). Nothing, it came out Rs=0, which is absurd, because that would mean Vgs=-6v, so Id=0.

I honestly have no idea what to do next. I've been at this for over 4 hours.