Vector Math for Raytracer
I think there might be a misprinting in the book. I am getting this

$((A-C) + tB)\cdot((A-C) + tB) = R\cdot R$ 

Let  A-C = Y

$(Y + tB)\cdot(Y + tB) = R\cdot R$

$Y\cdot Y + Y\cdot tB + tB\cdot Y + t^2B\cdot B = R\cdot R$

Substituting back 

$(A-C)\cdot(A-C) + 2t * B\cdot(A-C) + t^2B\cdot B = R\cdot R$