x2+y2+z2-x(al1+bl2+cl3)-y(am1+bm2+cm3)-z(an1+bn2+cn3)=0 solve this equation

I see an equation of the form

x^2 + y^2 + z^2 + ax + by + cz = 0

which looks like the equation of a sphere which has been translated.
What are you solving for?