There are three mistakes with your code:
- The
addmargin environment provides an optional and a mandatory argument, but you are trying to use two mandatory arguments. - As the name already says, the
addmargin environment adds the values of the arguments to the left and right margin. So to make the margins smaller, you need to use a negative value. - The arguments of
addmargin should be length or dimensional values not dimensional expressions. For dimensional expressions, you can use \dimeval{…}, \dimexpr …\relax or the calc package.
So a solutions using addmargin would be:
\documentclass{scrbook} \usepackage{blindtext} \usepackage[textwidth=12cm, textheight=22cm, includehead=true, includefoot=true, headsep=1.2\baselineskip, marginparsep=0.8cm, marginparwidth=4.2cm, inner=2cm, top=1.5cm ]{geometry} \begin{document} \blindtext % \begin{equation} E = m c^2 \end{equation} % \blindtext % \begin{addmargin*}[0pt]{-\dimeval{\marginparsep+\marginparwidth}} \setlength{\belowdisplayshortskip}{0pt}% This IMHO improves vertical alignment \begin{equation} EEEEEEEEEEEEEEE = mmmmmmmmmmmmmmmmmmmmmmm c^2 \end{equation} \end{addmargin*} % \blindtext \end{document}

This also works when using another class. In this case you just have to add package scrextend to be able to use the addmargin environment.
BTW: If you want all equation environments to use the extended width, you could use environment hooks, e.g.:
\documentclass{scrbook} \usepackage{blindtext} \usepackage[textwidth=12cm, textheight=22cm, includehead=true, includefoot=true, headsep=1.2\baselineskip, marginparsep=0.8cm, marginparwidth=4.2cm, inner=2cm, top=1.5cm ]{geometry} \AddToHook{env/equation/before}{% \begin{addmargin*}[0pt]{-\dimeval{\marginparsep+\marginparwidth}} \setlength{\belowdisplayshortskip}{0pt}% } \AddToHook{env/equation/after}{% \end{addmargin*} } \begin{document} \blindtext % \begin{equation} E = m c^2 \end{equation} % \blindtext % \begin{equation} EEEEEEEEEEEEEEE = mmmmmmmmmmmmmmmmmmmmmmm c^2 \end{equation} % \blindtext \end{document}
See “LaTeX's hook management” for more information.