Is this regression possible?

I am considering starting a research project but before I invest lots of hours into it I need to know if I will actually be able to do the math after collecting all the data.
I know the formula to describe what I am measuring (Y) is of the form
Y= (bB+lL+pP+c-dD-vV-qQ-k)/(bB+lL+pP+c+2)

Where I know the input variables B,L,P,D,V,Q and I am trying to find the coefficients b,l,p,d,v,q and constants c,k

If it is not possible to find the 8 coefficients by regression I could always get 8 equations and solve them simultaneously (I believe iterative methods exist for this) but that is less flexible as I can't weight data or use more than 8 samples.

Consider the relationship on the form :
(bB+lL+pP+c+2)Y= (bB+lL+pP+c-dD-vV-qQ-k)
b(BY-B)+I(LY-I)+p(PY-P)+c(Y-1)+dD+vV+qQ+k=-2Y
Then, you can perform a linear regression in order to compute aproximates of b,l,p,c,d,v,q,k, with known data (BY-B), (LY-I), (PY-P), (Y-1), D, V, Q, 1 and -2Y