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documentclass{article} 



newcommand{dd}[1]{mathrm{d}#1}



begin{document}

begin{equation}

Delta A_2 = x^2

end{equation}

This code puts a (1) next to this equation, and numbers later equations accordingly. If I want to reference this equation, say with:

And as you can see in Eq. #, 

how would I link it so that if the equation number later changes, I don't have to update the text?

You can simply use label{...} within the equation environment and ref{...} to refer to it.

For more info, see here: https://en.wikibooks.org/wiki/LaTeX/Labels_and_Cross-referencing.

And remember to compile twice, the first time you'll get ?? instead of the ref.no., but don't worry, it's normal, the second time you'll get the correct number.

documentclass{article} 



begin{document}

Equation ref{eq:myeq} blah blah blah

begin{equation}label{eq:myeq}

Delta A_2 = x^2

end{equation}

end{document}

If you add another equation, LaTeX will manage the numbering:

documentclass{article} 



begin{document}

If I add another equation ref{eq:myneweq},  LaTeX{} will manage the numbering. 

begin{equation}label{eq:myneweq}

Delta A_1 = x

end{equation}

Equation ref{eq:myeq} blah blah blah

begin{equation}label{eq:myeq}

Delta A_2 = x^2

end{equation}

end{document}

You can just add label{yourlabel} after begin{equation}:

begin{equation}label{equ1}