Back in the good old days when I was trying to suss the ADF I was taught the 3 basic rules:-
1/ the NDB is permanently fixed to the head of the needle
2/ the a/c is permanently fixed to the centre of the needle
3/ all you can ever do as a pilot is drag the tail of the needle around the dial
As for orientation, figure what quadrant you're in (NE, SE etc) then what quadrant you want to be in, eg to intx 180 to the NDB you need to be in the N quadrant, then turn to make it happen.
I too can't do the sums to make the mathematical solution work.