How to typeset some text including math content in sans serif

Okay, I found a solution in embarrassingly short time after posting the question: The sansmath package provides the \sansmath command (and several environments) for this purpose.

I am yet curious to know if there is some solution that does not depend on an additional package.

\documentclass{article}
\usepackage{lmodern}
\usepackage{sansmath}
\newcommand{\SomeText}{This is some text with math stuff in it. 
    $x>5$, $a^2+b^2=c^2$}

\begin{document}
  \begin{description}
    \item[Roman:] \SomeText
    \item[Sans:] {\sffamily \SomeText \\ However, the math is still Roman.}
    \item[AllSans:] {\sffamily\sansmath \SomeText}
  \end{description}
\end{document}

Have a look at Make mathfont respect the surrounding family. There you’ll find a solution to change the math alphabet and also to make the normal font switches (like \sffamily) change the math font too.

Taken from there:

\documentclass[parskip=half]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage{lmodern}

\DeclareMathVersion{sans}
\SetSymbolFont{operators}{sans}{OT1}{cmbr}{m}{n}
\SetSymbolFont{letters}{sans}{OML}{cmbrm}{m}{it}
\SetSymbolFont{symbols}{sans}{OMS}{cmbrs}{m}{n}
\SetMathAlphabet{\mathit}{sans}{OT1}{cmbr}{m}{sl}
\SetMathAlphabet{\mathbf}{sans}{OT1}{cmbr}{bx}{n}
\SetMathAlphabet{\mathtt}{sans}{OT1}{cmtl}{m}{n}
\SetSymbolFont{largesymbols}{sans}{OMX}{iwona}{m}{n}

\DeclareMathVersion{boldsans}
\SetSymbolFont{operators}{boldsans}{OT1}{cmbr}{b}{n}
\SetSymbolFont{letters}{boldsans}{OML}{cmbrm}{b}{it}
\SetSymbolFont{symbols}{boldsans}{OMS}{cmbrs}{b}{n}
\SetMathAlphabet{\mathit}{boldsans}{OT1}{cmbr}{b}{sl}
\SetMathAlphabet{\mathbf}{boldsans}{OT1}{cmbr}{bx}{n}
\SetMathAlphabet{\mathtt}{boldsans}{OT1}{cmtl}{b}{n}
\SetSymbolFont{largesymbols}{boldsans}{OMX}{iwona}{bx}{n}

\newif\IfInSansMode
\let\oldsf\sffamily
\renewcommand*{\sffamily}{\oldsf\mathversion{sans}\InSansModetrue}
\let\oldbf\bfseries
\renewcommand*{\bfseries}{\oldbf\IfInSansMode\mathversion{boldsans}\else\mathversion{bold}\fi\relax}
\let\oldnorm\normalfont
\renewcommand*{\normalfont}{\oldnorm\InSansModefalse\mathversion{normal}}
\let\oldrm\rmfamily
\renewcommand*{\rmfamily}{\oldrm\InSansModefalse\mathversion{normal}}

\usepackage[textwidth=9cm]{geometry}

\begin{document}
\section{Inline-$m\alpha \tau h$}
Normal: A $Ax\alpha+\chi b$

\sffamily Sans: A $Ax\alpha+\chi b$

\bfseries Bold-Sans: A $ Ax\alpha+\chi b$

\normalfont Normal: A $ Ax\alpha+\chi b$

\bfseries  Bold: A $ Ax\alpha+\chi b$

\normalfont Normal: A $ Ax\alpha+\chi b$

\section{Display-$\mu\alpha\tau\eta$}
Text in roman family
\begin{equation}
     \sqrt{(a_1+a_2+\gamma)^2}=\sum_{i=1}^2 a_i + \gamma
\end{equation}

\sffamily
Text in sans family
\begin{equation}
    \sqrt{(a_1+a_2+\gamma)^2}=\sum_{i=1}^2 a_i + \gamma
\end{equation}

\sffamily\bfseries
Text in sans family, bold version
\begin{equation}
    \sqrt{(a_1+a_2+\gamma)^2}=\sum_{i=1}^2 a_i + \gamma
\end{equation}

\rmfamily\bfseries
Text in roman family, bold version
\begin{equation}
    \sqrt{(a_1+a_2+\gamma)^2}=\sum_{i=1}^2 a_i + \gamma
\end{equation}
\end{document}

An addition to @Tobi's excellent answer, if you need to use helvetica for the Sans serif fonts:

\DeclareMathVersion{sans}
\SetSymbolFont{operators}{sans}{OT1}{cmsmf}{m}{n}
\SetSymbolFont{letters}{sans}{OML}{cmssm}{m}{it}
\SetSymbolFont{symbols}{sans}{OMS}{cmsssy}{m}{n}
\SetMathAlphabet{\mathit}{sans}{OT1}{cmssm}{m}{sl}
\SetMathAlphabet{\mathbf}{sans}{OT1}{cmsssy}{bx}{n}
\SetMathAlphabet{\mathtt}{sans}{OT1}{cmssex}{m}{n}
\SetSymbolFont{largesymbols}{sans}{OMX}{cmssex}{m}{n}

(taken from sansmathfonts.sty from the sansmathfonts package). This then blends in with text that is typesetted with \fontfamily{phv}\selectfont\mdseries (remember to still use \sffamily for the maths)

Example: