Full Swivel TV Mount on Vertical Studs
It sounds like maybe there used to be a window where you're putting the TV, is that possible?  That would explain the framing you're hitting.  

Anyway - it sounds like you put 2x8s from the top of what used to be the window to the bottom.  This will be more than enough support, as long as the 2x8s were attached with big screws, lag screws, lumber screws, etc.