'eloquent explanation' is correct and usable in written English.
It is typically used to describe an explanation that is expressed in a clear and persuasive manner. For example, "The professor gave an eloquent explanation of the different functions of the heart."
Photograph: Reuters It is a vice of second-rate art to come with its own eloquent explanation attached.
Then Jeb Bush piped in with an eloquent explanation of why he did not think that was wise because it would take away much needed money for highways.
Quite what it involved is uncertain, but in 1821 he produced an eloquent "Explanation" in which, he wrote, "it is as impossible for it to stand still as it is for a bird to fly without wings".
It sprang to mind again as I read the letter that Tim Sanford, the artistic director of Playwrights Horizons, sent to some subscribers of that Off Broadway theater, offering a long and eloquent explanation (with a spoonful or two of apology) of the theater's decision to mount "The Flick," the new play by Annie Baker.
David Remnick wrote Sunday about Havel's life, which provided our most eloquent explanation of why totalitarianism must be total, why it depends, at bottom, not on the number of guns and tanks at the regime's disposal, but on the consistent denial of reality, on the mixture of fear and ritual that raise the costs for any one person to dare to acknowledge that the emperor wears nothing at all.
Standing alone beneath the fore topsail, I recited the simplest and most eloquent explanation of what was happening, from Coleridge's Rime of the Ancient Mariner.
As a writer, I'd like nothing better than for eloquent explanations and expert insights to create an entirely persuasive movement anatomising technology's opportunities and perils.
While some chapters certainly call for governments to better support the interwoven interests of pastoralists and Asian drylands, others provide eloquent explanations of why the current methods of scholarship and governance must be revised for the sake of both pastoralists and the land.
The budget presentation given to the press by Alan Krueger, who chairs the President's Council of Economic Advisors, was as eloquent an explanation of our economic situation as has been given from the White House in many decades.
Hamdan's eloquent and restrained explanation for his boycott was the most poignant event in his hearing, but it was not the most explosive.
"I tend to explain my songs," Nneka said onstage, and for a few she was more eloquent in those explanations than in the songs themselves.
