I am working with some quadratic equations(from my notes) and I am having trouble understanding what is going on.

For one I have....

1.

3y^2-6y-2=0

then it goes to

2.

y=[6+√(36+24)]/6 and I am not sure what happened there. EDIT:woops forgot about the quadratic formula :P

then

3.

y=6+√(4*15) ->I don't know what happened to the 6 that was on the bottom.

4.

y=(3+√15)/3 ->where did the 4 go? where did these 3's come from?

5.

y=1+[3/(3+√15)] ->still confused

6.(3+√15+3)/(3+√15) ->I actually know what happened here

7.

y=[(6+√15)(3-√15)]/[(3+√15)(3-√15)] ->What??!?! No clue how we got from step 6 to 7.

8.

y=(18+3√15-6√15-15)/(9-15) ->I can see what happened here

9.y=3-3√15 ->what happened to the 9-15 on the bottom

ps. I am pretty sure I copied the notes down correctly but maybe I am wrong.