how to verify if an equation already exists (and whom to credit for it)

Say I’m writing an article on a mathematical topic…and I wish to crisply articulate how the distance between two consecutive squares is the sum of the two square roots (( ex: 20^2 is 400, which is 39 more than 19^2 (361), and 39 = 20 + 19 )).

So I include the equation: (x+1)^2 – (x)^2 = 2x + 1

Now, because this equation involves rather elementary subject matter, I assume someone else has most likely authored such an equation.

But how does one verify for sure if someone else has already authored a particular equation ?

And, moreover, how does one ascertain whom to credit when one wishes to include this equation in an article ?

I entered this equation (surrounded by quotation marks) into the Google and did not get a direct hit.

Might there be a database of existing equations or some similar resource ?