The phrase "backroom deal" is correct and usable in written English. It typically refers to a negotiation or agreement made between parties in private, and not publicly disclosed. For example, "The mayor was accused of making a backroom deal with the developers to build a new high-rise.".
This wasn't some insidious backroom deal.
There must be no backroom deal.
So what about a backroom deal?
"This was not a backroom deal.
Instant tweets make a mockery of the backroom deal-making essential to politics.
The promises of transparency have given way to the reality of backroom deal-cutting.
The investigation has drawn public attention to Mr. Ozawa's use of financing methods and backroom deal-making like those of the now discredited and demoralized Liberal Democrats.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia