Find the points of intersection of the line r=(0,5,3) +t(1,-3,-2) with the sphere x^2+y^2+z^2=6. Is the segment of the line between the intersection points a diameter of the sphere?

I'm not sure what I am doing wrong (obviously a lot) since I can't get the right answer with the back of my textbook. Please fix my errors and demonstrate the correct approach. Thanks!

x/1 = (y-5)/-3 = (z-3)/-2

x^2 = x=6

x^2-x-6=0

x=-3 or x=2