Settings need to be corrected on the HDTV and drivers, so the screen fits the size.
If both screens go black it's PC problem , if only one it's the TV problem.
You have to plug HDMI into the HDMI-DVI port only, that indicates a source where DVI output uses HDMI adapter.
Lastly, HDTVs are full of crap, and your HDTV model is on the mainstream side, i have UE40D6750 and it's not perfect either, but acceptable for TV stuff, HDD, allshare, watching SC2 tournaments (web browser sucks, slow, laggy, buggy, unstable, remote control responsivness total crap/firmware input detection horrible), crap for anything else.
You may get more deeper info on HDTVs them selfs on AVForums.com , before I bought mine i spent weeks researching.