Broadly speaking in a room like that you want the system on the long wall and sit opposite. In some cases it might help to have a second pair of speakers that shoot down the area; in other words on the short wall, to get good sound for, say, casual dining. If it were me I'd have them on the den side.
You can do 5.1/7.1 if you're willing to have ceiling mounted speakers for side/rear in the main system opposite your screen. By "ceiling mounted" I don't necessarily mean ceiling speakers; by way of an example you could try something like the Gallo spheres mounted a foot or whatever from the ceiling. An important consideration for some would be the overall appearance, so keep in mind whatever you choose, if it's hanging, you will see all sides of the speaker. A lot of speakers don't look that nice from behind.
The good news is the side/rears are not particularly critical response-wise so you shouldn't feel the need to worry about not covering them up somehow for asthetics. Even a lantern shade of the right kind might work. You are going to need to be creative if you want it to look good, but if you think outside the box, it's not impossible.
With both the long-wall speakers and if you choose, the supplementary ones mounted on the short wall for casual music, be wary of placing the speakers too far apart. For the main system, start with them 1/2 the distance apart vs your listening position (ie no more than 6' apart for a 12' listening distance, in practical terms the listening distance in your example room will be less so adjust accordingly), and if there's a hole in the middle, move them closer or toe them in, or both.
For the "casual listening" speakers, somewhat the same but even more critical because they will be throwing down such a long "tunnel", start with them at least as far from the long side walls as they are apart (ie on the short wall 'thirds"). Toeing them in probably won't help, so if you need to make adjustments, closer together is the way to go. Don't be surprised if they end up very close together, that's pretty common in my experience.
Should give you some things to think about and get started on. There is always a danger in assuming there are hard-and-fast rules, but I've had similar rooms and the solutions I've outlined worked well. If the room was a bit wider, you probably could get good results either on the short wall or midway along the long walls firing towards the den area, with your listening position on the short wall or in the middle of the room pointing towards the short den-side wall. Whether that's an option worth exploring is something you will have to figure out based on your own needs for traffic, appearance, etc.
