The golden ratio is significant for the visual art but, imho, not so much for the speaker placement due to the complex interaction between the speakers and the room, room setup and the horizontal dispersion pattern of the speaker drivers especially tweeters. Rather, there is a more flexible tool called LOTS (Loudspeaker Optimization Techniques for Soundstage) introduced by Ron of New Record Day. In my room where the width (W) is 14 ft and the depth (L) is 18 ft, the golden ratio triangle is a special case of the LOTS positions. First, the speaker positions from the golden ratio triangle are within the LOTS tracks (see diagram) without exception (because 0.276W is between W/4 and W/3). Second, in this combination of W and L, the listening positions suggested by these two methods coincide.
Based on my experience, the most probable LOTS positions locate between the minimum distance of 3 ft to both the front / side walls and the vertices of the equilateral triangle. With that being said, you probably do not need to experiment all the way from the front wall to the L/3 position within the LOTS tracks as suggested by Ron. The min. distance of 3 ft is suggested by Tarun of A British Audiophile based on the theory that “any sound that hits your ears from the reflective surfaces that is not delayed by 5 millisecond is perceived as the direct sound.” The speed of sound at the sea level is approximately 1100 ft/sec and the half of the distance travelled in 5 millisecond is just under 3 ft.
So, using these empirical rules, I end up with the speaker positions just a bit wider than the LOTS tracks with slight toe-in. I felt, a bit wider separation between the speakers helps maximize the soundstage (SS) width. I also felt further separation from the front wall gives a bit better SS depth but 3 ft is maximal separation I could live with in my room. So I sacrifice a bit SS depth to make the room more functional for other purposes. Again, it is a trade-off I am willing to live with in my room.