So in this problem we need to do some addition. 
take the starting balance (-200) and add it to the amount you paid back (30) 
-200 + 30 = -170
        
                    
             
        
        
        
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be 

.
You're minimizing 

 subject to the constraint 

. Note that 

 and 

 attain their extrema at the same values of 

, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is

Take your partial derivatives and set them equal to 0:

Adding the first three equations together yields

and plugging this into the first three equations, you find a critical point at 

.
The squared distance is then 

, which means the shortest distance must be 

.
 
        
        
        
                    x + 1
         __________
3x+2 I 3x² +5x -3
           3x² +2x
           ----------
                    3x -3
                    3x+2
                    --------
                          -5 is the remainder