Problem understanding MOSFETs
A MOSFET is a transconductance device. That means you get amps out for volts in. It also means that any formula you see contains \$I_{D}\$ (amps out) and \$V_{GS}\$ (volts in) rather than \$V_{DS}\$ (volts out). 

If you want a formula that contains \$V_{DS}\$, use the formula that contains \$I_{D}\$ and multiply it by the circuit resistance in the drain connection.