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\documentclass{article}
\usepackage{mathtools}   % lädt »amsmath« nach

\begin{document}
  \begin{equation}
    \begin{aligned}
      \rho \frac{\partial u_i}{\partial t^2} &= \frac{\partial}{\partial x_j}\left(\lambda \theta \delta_{ij}+2\mu \epsilon_{ij}\right)\\
      &= \frac{\partial}{\partial x_j}\left(\lambda \theta \right) + \frac{\partial}{\partial x_j}\biggl[\mu \left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right)\biggr]\\
    \end{aligned}
  \end{equation}
\end{document}

\documentclass{scrreprt} 
\usepackage[ngerman]{babel} 
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}	

\usepackage{blindtext} 
\usepackage{amsmath}

\begin{document}

\blindtext

%\begin{equation} 
\begin{align}
\begin{split} 
\rho \frac{\partial u_i}{\partial t^2} & =  \frac{\partial}{\partial x_j}\left(\lambda \theta \delta_{ij}+2\mu  \epsilon_{ij}\right)\\ 
& = \frac{\partial}{\partial x_j}\left(\lambda \theta \right) + \frac{\partial}{\partial x_j}\biggl[\mu \left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right)\biggr]\\ 
\end{split}
\end{align} 
%\end{equation} 

\blindtext
 
\end{document}

\begin{equation}
\begin{align}
\rho \frac{\partial u_i}{\partial t^2} & =  \frac{\partial}{\partial x_j}\left(\lambda \theta \delta_{ij}+2\mu  \epsilon_{ij}\right)\\
& = \frac{\partial}{\partial x_j}\left(\lambda \theta \right) + \frac{\partial}{\partial x_j}\biggl[\mu \left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right)\biggr]\\
\end{align}
\end{equation}