paragraph 1
\begin{equation*}
equation 1
\end{equation*}
paragraph 2
paragraph 3
\begin{equation*}
equation 2
\end{equation*}
paragraph 4
paragraph 5
There's an inline equation in paragraph 4 which I keep on one line by preceding it with \linebreak. However, I have found out that sloppypar, along with surrounding the equation in brackets, is preferable as it selects better line breaks, i.e. \begin{sloppypar} paragraph 4 \end{sloppypar} and ${a=b}$. The problem is that this increases the vertical spacing between equation 2 and paragraph 4 (but not to paragraph 5). Similarly, enclosing paragraph 3 in sloppypar increases the spacing to equation 2 (but not to paragraph 2).
By starting paragraph 4 with \sloppy instead, the spacing to equation 2 is not increased, but the spacing between equation 1 and paragraphs 1 and 2 is increased; perhaps it makes the whole document sloppy?
How do I make the paragraph sloppy without such adverse effects?
Edit: here's code to reproduce the sloppypar issue.
\documentclass[12pt,a4paper,final]{article}
\usepackage{mathtools}
\setlength\parindent{0pt}
\setlength{\parskip}{10pt}
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Cras arcu arcu, volutpat sed rhoncus porttitor, tincidunt at eros. Praesent at leo non arcu rutrum maximus in ut nibh. Ut rutrum efficitur tincidunt. Etiam fermentum nunc vitae sapien mattis cursus. Proin venenatis nulla velit, at dictum risus commodo non. Pellentesque semper
\begin{equation*}
\frac{lorem}{ipsum} = dolor\frac{sit}{amet}
\end{equation*}
Donec malesuada mollis mauris id fermentum. Vivamus arcu felis \linebreak $lorem = ipsum+dolor$.
Vestibulum ornare euismod est a rutrum. In dictum elit dapibus velit consequat, vitae accumsan purus fermentum. Morbi aliquam, purus eget euismod interdum, arcu mi molestie turpis, ut sodales urna dolor pharetra dui.
\end{document}
Compare to \begin{sloppypar}Donec malesuada mollis mauris id fermentum. Vivamus arcu felis ${lorem = ipsum+dolor}$.\end{sloppypar}.
sloppyparas a last resort. Don't worry about such problems until your document is in final form as regards to the text. Anyway, debugging the issue needs code that reproduces it.\begin{equation}..\end{equation}but you mean you put the braces inside inline math, there are better ways of stopping line breaking, I'll link to an answer. You have added an example but it is very hard to give sensible improvements to the line breaking if the text and math just has fake latin