For the frame around theorem-like structures, one possibility is to use mdframed
and amsthm
; for a simple frame around equations, empheq
-style, it's enough to say something like:
\newcommand*\mymathbox[1]{%
\fcolorbox{ocre}{mygray}{\hspace{1em}#1\hspace{1em}}}
and then use box=\mymathbox
in the optional argument of empheq
. A complete example:
\documentclass{book}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{empheq}
\usepackage{bookman}
\usepackage[framemethod=tikz]{mdframed}
\definecolor{ocre}{RGB}{243,102,25}
\definecolor{mygray}{RGB}{243,243,244}
\newcommand*\mymathbox[1]{%
\fcolorbox{ocre}{mygray}{\hspace{1em}#1\hspace{1em}}}
\newtheoremstyle{mystyle}
{\topsep}
{\topsep}
{\normalfont}
{}
{\sffamily\bfseries}
{.}
{.5em}
{{\color{ocre}\thmname{#1}~\thmnumber{#2}}\thmnote{\,--\,#3}}%
\theoremstyle{mystyle}
\newmdtheoremenv[
backgroundcolor=mygray,
linecolor=ocre,
leftmargin=20pt,
innerleftmargin=0pt,
innerrightmargin=0pt,
]{theo}{Theorem}[section]
\begin{document}
\chapter{Test chapter}
\section{Test section}
\begin{theo}[Name of the theorem]
In $E=\mathbb{R}^n$ all norms are equivalent.
\begin{align}
a &= b\\
E &= mc^2 + \int_a^a x\, \mathrm{d}x
\end{align}
\end{theo}
\begin{empheq}[box=\mymathbox]{align}
a&=b\\
E&=mc^2 + \int_a^a x\, \mathrm{d}x
\end{empheq}
\end{document}

In a comment, it has been requested to have a framed box similar for those for theorems in my previous solution, but for math expressions; one possibility here is to use the tcolorbox
package:
\documentclass{book}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{bookman}
\usepackage[most]{tcolorbox}
\definecolor{ocre}{RGB}{243,102,25}
\definecolor{mygray}{RGB}{243,243,244}
\tcbset{myformula/.style={
arc=0pt,
outer arc=0pt,
colback=mygray,
colframe=ocre,
boxrule=0.4pt,
left=2pt,
right=2pt,
highlight math style={
arc=0pt,
outer arc=0pt,
colback=mygray,
colframe=red.
}
}
}
\begin{document}
\chapter{Test chapter}
\section{Test section}
\begin{tcolorbox}[ams equation,myformula]
E = mc^2 + \int_a^a x\, \mathrm{d}x
\end{tcolorbox}
\begin{tcolorbox}[ams align,myformula]
a &= b \\
E &= mc^2 + \int_a^a x\, \mathrm{d}x
\end{tcolorbox}
\end{document}

Or, using mdframed
again,
\documentclass{book}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{bookman}
\usepackage[framemethod=tikz]{mdframed}
\definecolor{ocre}{RGB}{243,102,25}
\definecolor{mygray}{RGB}{243,243,244}
\newmdenv[
innertopmargin=0pt,
backgroundcolor=mygray,
linecolor=ocre,
innerleftmargin=0pt,
innerrightmargin=0pt,
leftmargin=10pt
]{mymath}
\begin{document}
\chapter{Test chapter}
\section{Test section}
\begin{mymath}
\begin{align}
a &= b\\
E &= mc^2 + \int_a^a x\, \mathrm{d}x
\end{align}
\end{mymath}
\end{document}
