It was an accident that could no be avoided, so it was settled out of court.
It was an accident that could no be avoided, so it was settled by compromise.
"示談" 英語で "settlement out of court" ("法廷外での解決" という訳出で ) または, "settlement by compromise" ("妥協による決済" という訳出です ).
どうしても避けられない事故だったので : It was an accident that could no be avoided.
示談で方がつきました : so it was settled out of court / so it was settled by compromise.