Ray/Quadric Intersection

Assume a ray with origin R0 = (x0,y0,z0)
and direction Rd = [xd,yd,zd], Rd a unit vector.
R(t) = R0 + tRd
Quadric Surface PT QP = 0

Substituting R(t) = R0 + tRd into PT QP = 0 and solving for t:

-Bq +/- [[radical]]( Bq2 -4AqCq)
t = -----------------------------
2Aq