Hi,
I play 10NL equivalent. This is a crazy hand (crazy for me anyway). I am not sure I played this correctly.

SB is a somewhat loose reg, BB is an unknown but tight player, BU is unknown. I think my image is slightly LAG, but I don't get out of line too much. I am in CO with Qs Js. Stack sizes are the following:

BU: 53 BB
SB: 29 BB
BB: 97 BB
Hero (CO): 120 BB

Preflop I raise to 3BB, BU calls, SB calls, BB calls.

Flop comes As Ts 6h. It gets checked around to me. I bet 7BB, BU calls, SB min-raises (!), BB calls (!!), I shove, BU folds, SB calls, BB calls.

SB showed up with Ah Qh and BB showed up with 66.

My thought process was that even against sets or two pairs, I have 12 outs, and most of them are to the nuts. And the amount of money in the pot means that I shouldn't need more than, say 30-ish percent equity to make the shove profitable. I checked Equilab, and I have 35% equity here against these exact hands.

Did I play this correctly?