Coloured shadowed boxes around equations

Here are some additions using tcolorbox. You can use a macro \tcbhighmath which is designed for such a task. The style can be varied also by options given to this macro.

\documentclass{article}
\usepackage[skins,theorems]{tcolorbox}
\tcbset{highlight math style={enhanced,
  colframe=red,colback=white,arc=0pt,boxrule=1pt}}
\begin{document}
\begin{equation}
\tcbhighmath[drop fuzzy shadow]{\Delta = b^2 - 4ac}
\end{equation}

\begin{equation}
\tcbhighmath[boxrule=2pt,drop fuzzy shadow=blue]{E = m\cdot c^2}
\end{equation}

\begin{equation}
\tcbhighmath[boxrule=0.4pt,colframe=blue,drop fuzzy shadow=red]{a^2 + b^2} =
\tcbhighmath[arc=4pt,drop fuzzy shadow=green]{c^2}
\end{equation}

\begin{equation}
\tcbhighmath[boxrule=2pt,arc=1pt,colback=blue!10!white,colframe=blue,
  drop fuzzy shadow=red]{ \ln|x| = \int\limits_1^x t~dt }
\end{equation}

\begin{equation}
\tcbhighmath[fuzzy halo=1mm with blue!50!white,arc=2pt,
  boxrule=0pt,frame hidden]{ \ln|x| = \int\limits_1^x t~dt }
\end{equation}

\tcbset{myinner/.style={no shadow,shrink tight,extrude by=1mm,colframe=blue,
  boxrule=0.4pt,frame style={opacity=0.25},interior style={opacity=0.5}}}
\begin{equation}
\tcbhighmath[drop fuzzy shadow=red!50!yellow,colback=red!20!white]{
  \tcbhighmath[myinner]{\Delta} =
  \tcbhighmath[myinner]{b^2 - 4ac}}
\end{equation}

\end{document}

I can't say I know all the ins and outs of tcolorbox, but this demonstrates that it works with equation material.

\documentclass{article}
\usepackage{tcolorbox}
\begin{document}
Testing
\begin{equation}
\tcbox[nobeforeafter]{\( \Delta = b^2 - 4ac \)}
\end{equation}
\end{document}