What is the best way to position 5.1 surround sound speakers for a TV in the corner of the room?

Looking at your room layout, and accepting that you can't move things around, I think you've pretty much made the best of it. You might want to consider putting the front speakers on either side of the TV pointing slightly outwards? I'm not sure on the height, but if you are floor mounting the speakers, the RL could go closer to the corner, up on the picture, and the RR might go under to pool table on the right.

Not ideal, but once again making do. I probably don't need to say this, but if you could move the tv, sofa and exercise machine, you could have a near perfect installation. I had a similar issue and bit the bullet and moved the room around, which involved builders!

It was actually well worth the hassle.

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