You could load the mathtools
package and use its \splitdfrac
macro to split the numerator across two lines.
A separate comment: Do encase all six decimal commas in curly braces, in order to prevent TeX from interpreting as punctuation marks.

\documentclass{article}
\usepackage{mathtools} % for '\splitdfrac' macro
\begin{document}
\begin{equation}
a = \sqrt{\frac{\splitdfrac{(20{,}1-20{,}06)^2 + (20-20{,}06)^2+(20-20{,}06)^2}{%
+(20-20{,}06)^2+(20{,}2-20{,}06)^2}}{5}}
= 0{,}0289
\end{equation}
\end{document}
Addendum: You may also want to consider replacing \frac
with inline-fraction notation and replacing \sqrt{...}
with \{...\}^{1/2}
notation. This would allow you to use a multline
environment.

\documentclass{article}
\usepackage{amsmath} % for 'multline' env.
\begin{document}
\begin{multline}
a = \smash[b]{\Bigl\{}\bigl[
(20{,}1-20{,}06)^2 + (20-20{,}06)^2+(20-20{,}06)^2\\
+(20-20{,}06)^2+(20{,}2-20{,}06)^2\bigr]\big/5
\smash[t]{\Bigr\}^{1/2}} % \smash[b]{...} and \smash[t]{...} for more compact appearance
= 0{,}0289
\end{multline}
\end{document}