"believable explanation" is correct and usable in written English.
You can use it when you need to describe a plausible explanation for something. For example, "He provided a believable explanation as to why he was late for the meeting."
Another, and perhaps more believable, explanation is the business model problem.
This account, from a friend of Mr Johnson, is a believable explanation, but it represents only a partial account of why he is acting now.
In the movie, events take place against Veronica's 10-year reunion, which provides a believable explanation for the rotating door of high school-era regulars.
In fact, the testimony offered by Page and Strzok about the text presents a straightforward and believable explanation for a message that's become a shorthand for Trump's claims about what he says is a prejudiced investigation against him.
Having taken a good look at Amazee's size and scope, its logo, the believable explanation of how they came up with the name and particularly its current activities and future plans, I think Amazon is looking ridiculous going after them.
This is a highly reasonable and believable explanation for why Peter Mansbridge would be speaking to a CAPP crowd.
Xunzi thus presents a believable utilitarian explanation for the creation of social institutions.
Sensibly prioritising straight-faced weirdness over goofy gags, writer/director Baena keeps things just the right side of believable, eschewing explanation in favour of cracked domesticity.
Ultimately, Nicolau found Glass's version of events more believable than the explanations given by Douby, Miller and Ringel, which he found inconsistent.
When he broke a bone, the explanation was believable - he'd fallen off his bike.
Given what we know about sexsomnia, Copland's explanation is believable.
