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I need to add some comments in formula without changing the size of brackets. I was trying underbrace and some code of this forum, but did not succeed in reformatting my formula.

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\left[ \frac{1}{4} + \underbrace{ \frac{\delta(E)}{1+\frac{\alpha(E)}{2 \pi}} \frac{1}{K_{m}} x_{m}^{2} \frac{\frac{1}{4}\overline{\lambda}_{w0}}{R_{m}}}_{\frac{3}{4}~\mbox{nach Gl.~\ref{eq:Arnold4}, wenn {\overline{\lambda}_{w0}=4\overline{\lambda}_{{\rm c}}} \right]
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If you don't like scaling your brackets manually, you could "hide" the height of that underbrace and the note from LaTeX, using \smash. The obvious disadvantage (compared to manually scaling brackets) is that you will need to insert some extra spacing after the equation, to prevent the next paragraph from overlapping.

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\newcommand\smashUnderNote[2]{\vphantom{#1}%
  \smash{\underbrace{#1}_{\mathclap{#2}}}}

text text text text text text text text text text text text text text
text text text text text text text text text text text text text text 
text text text text text text text text text text text text text text 
text text text text text text text text text text text text text text 

$$\left[
  \frac{1}{4} +
  \smashUnderNote{
    \frac{\delta(E)}{1+\frac{\alpha(E)}{2 \pi}}
    \frac{1}{K_{m}} x_{m}^{2}
    \frac{\frac{1}{4}\overline{\lambda}_{w0}}{R_{m}}
  }{
    \frac{3}{4}~\mbox{nach Gl.~4, wenn }
    \overline{\lambda}_{w0}=4\overline{\lambda}_{{\rm c}}
  }
\right]$$
\vspace{1\baselineskip}

text text text text text text text text text text text text text text 
text text text text text text text text text text text text text text 
text text text text text text text text text text text text text text 

\end{document}

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