How do I compute \$V_{out}\$ in a MOSFET?
The following should provide enough material to allow you to unlose your lost lecture. If you just attempt to use it to plug in figures to solve a single assignment problem you will not gain much overall. The following is a Potpourri and you will need to sort out which is relevant. 

Best would be to "unlose" that lecture and/or get a proper understanding of the subject either from a textbook or a friend or a lecturer. Just having somebody help you plug numbers into equations like that isn't going to help you past the current assignment, at best.  

Here is a page that MAY help you with what you are doing.
 Slide 4 at the bottom of page 2 provides the information below. I have edited it somewhat to display better here and retain only what seemed relevant - see referred to page for extra information.

What this does is relate most of the parameters that you have in such a way that you should be able to plug the results into the diagram that you have.
 YOU have to decide if this satisfies hat you really need. You may need to think creatively to link some parameters as naming conventions seem slightly different. 


Drain Current, MOS transistor, in Saturation,  Long Channel


IDSAT
= K’n
/2  *  W/L (VGS
–VT 
)
2
(1 +   λVDS
)  
K’
n
= µn
Cox 





Also of possible use are These notes  

Also this annoying SCRIBD document - page 5 especially MAY be of use





And this Fairchild application note gives a somewhat simplistic but possibly quite useful guide.

Including

The following calculations derive how Gate Length “W”
effects RON.   


ID = (µn
COX) W/L [(VGS − VT) VDS − 1/2VDS^
2
]  

Where:
µn
= Electron mobility, (the ease with which electrons drift
in the material)
COX = Oxide capacitance
W  = Length of the gate (see Figure 1)
L  = Width of the gate (see Figure 1)
RON = On Resistance or resistance drain-to-source
ID = Drain current  


RON can be derived by taking the partial derivative of ID
over VDS where all other variables are considered constant.  


RON = 1/(µn
COX W/L)(VCC − VIN − VT))    

Where:
VDS = 0      


Therefore:  


RON = 1/(µn
COX W/L)(VGS − VT)     

Where
VS = VIN and VG = VCC    


Therefore (Equation 1):  


RON = 1/(µn
COX W/L)(VCC − VIN − VT)