successfully with unsolvable conflict is to increase the number of positive interactions to navigate the conflict when it arises. In addition, there are two broad classes of tools you can use to help teams navigate unsolvable conflict and turn it into a positive force for growth, or at least greater tolerance. They are: avoid misunderstanding build-up and use a shared vision.
Avoid misunderstanding build-up
Have you ever noticed that team members sometimes talk past one another? You may notice that they talk more than they listen, leaving true understanding behind. Or, maybe a voice has yet to be heard. Someone has something to say, but is not ready to risk speaking up. Without knowing this, the team moves on and leaves that team member in the dust.
As their coach, you note these things because you are paying attention to the quality in the conversation, but the team - embroiled in the work - probably doesn't notice. They need you to help tune their ears so they can learn to listen for quality in the conversation. When they do this, they will avoid misunderstanding build-up and they will increase the positivity in the relationships. All of this makes unsolvable conflict livable.
There are two simple tools you can teach them to help avoid misunderstandings and, as a by-product, increase the positivity in the group: consent check and consensus check. Consent check is used when it sounds like all the voices that want to be heard are being heard and the group is generally moving toward a shared conclusion. Consensus check is used when all voices are not being heard and it is unclear whether the team is moving toward a shared conclusion.
Let's say you are in a retrospective and the team is discussing whether to change their standup time to 1pm. Through the conversation, you notice that most people have spoken and no one has been talked-over or ignored. The general energy of the group is upbeat and it seems they are in sync with one another. In this case, I might ask for a consent check: "Is there anyone who objects to moving the standup to 1pm?" This question is purposely phrased in the negative, to give explicit permission for a team member to speak up if there is an objection.
The conversation about moving the standup time to 1pm could take a different tone. Let's say that some of the team members are in favor of moving the standup time and have spoken about the virtues of doing so. Others have raised minor concerns and they have been discussed. At one point, someone tried to get a word in edge-wise and was not successful. You have a gut feeling that the team is not moving together in the conversation. You think that there might be something unspoken here - some need or concern that is left unsaid. In this case, I would call for a consensus check. Professional facilitator and coach, Jean Tabaka, offers us the "Fist of Five" method of checking consensus.  To do it, say something like, "Let's see where we are with this idea of moving the standup to 1pm. Let's do a consensus check. Ready? 1, 2, 3." On "3", each team member holds up a hand showing one to five fingers, to correspond with their level of agreement to the statement. Paraphrased from Jean Tabaka, here's what they mean:
Five fingers: I love this idea. I wish I had thought of it myself.
Four fingers: I'm happy with this idea and am glad we came up with it.
Three fingers: I