"we both acknowledged" is correct and usable in written English.
You can use it when referring to a mutual understanding between two or more people, or to refer to something that was mutually accepted by all parties involved. For example, "We both acknowledged that the decision we'd made was the best for the company."
With a certain sheepishness, we both acknowledged our acquaintance in that distant past.
When we married, we both acknowledged that he was going to die before me, but I thought that we would have at least 10 years.
"I think what we both acknowledged is, is that when you're in a tough primary battle you say things that afterward you may end up thinking, that may have been a little intemperate.
As it proved, among my best memories of the filmmaking are the conversations (drunken or otherwise) I had with Fred, in which we both acknowledged, I think, that, different as film directors and novelists are, our abiding obsession was the same: the mysteries of storytelling - of timing, pacing and the exactly judged release of information and emotion.
At our last tea together in the Lords restaurant – and we both acknowledged that it was probably our last – I was again struck by how, despite his disabilities, despite all his successes, he was still the same Jack I had met in the pub long ago.
"He and I simply have not had time to sit down and finalise his contract although we have both acknowledged to each other on several occasions that we must - and we will.
We both acknowledge and encourage each other's fantasy life, so there's never a feeling that something is private or secret.
I think we both acknowledge that's the case".
For the record, we both acknowledge Beyoncé's talent and appreciate why so many people, and women in particular, are applauding Lemonade, and perhaps seeing themselves in it.
"While we both acknowledge our own human sinfulness, Derek has taken full responsibility for the events which led to this decision," the statement said.
We must ask ourselves, how do we both acknowledge the persistent disparities and concerns of the past while also looking to the future for continued upward mobility for all?
