Oh my.

I guess you have 3 choices. I'll list in order of preference

A) Hire Pro
B) Use a piece of 3/4" Birch (Finished) plywood, long enough to fully span 2 studs, apply a little liquid nail and securely screw it to the wall.
C) Screw through the face of the plasma directly to the studs and return the articulating arm
D) Buy 2 rolls of duct tape and fasten bracket securely to the wall.

NOTE: If you chose either C or D, keep small kids and dogs away and immediately notify you insurance carrirer of an impending claim.