When you know you have a sphere and a box colliding with each other, why don't you use the implicit representation of the sphere? ( (x-x0)^2 + (y-y0)^2 + (z-z0)^2 = r^2 ), where (x0,y0,z0) is the origin of the sphere.
... and a transformed box, where the box is either an object oriented bbox, or you just use an axis aligned bbox, and transform the sphere into your local AABB space, which might make the collision detection easier.
Maybe this applies to your case, if not, I apologize...
... though finding the point(s) of intersection here is not so intuitive.