If an equation is too long to fit on a single line, you need to employ an alternative environment that allows for line breaks. The multline environment (provided by the amsmath package) would seem to be well suited for your equation.
I would also replace all instances of . and * (dots and stars) with simple thinspaces.

\documentclass{article}
\usepackage{amsmath} % for "multline" environment
\begin{document}
\noindent
before: \texttt{equation} environment
\begin{equation}
\frac{n_d}{m_d}.\psi\left(x+1,y\right)+\frac{n_d}{m_d}. \psi\left(x-1,y\right)-2. \left(\frac{n_d}{m_d}+\frac{m_d}{n_d}\right). \psi\left(x,y\right)+\frac{m_d}{n_d}. \psi\left(x,y+1\right)+\frac{m_d}{n_d}. \psi\left(x,y-1\right)=m_d*n_d*\frac{q}{\epsilon}\left(n-p-C\right)
\end{equation}
\bigskip\noindent
after: \texttt{multline} environment, no ``.'' or ``$*$'', no \verb+\left+ or \verb+\right+ directives
\begin{multline}
\frac{n_d}{m_d}\, \psi(x+1,y)+\frac{n_d}{m_d}\, \psi(x-1,y)
-2\, \Bigl(\frac{n_d}{m_d}+\frac{m_d}{n_d}\Bigr)\, \psi(x,y)\\
+\frac{m_d}{n_d}\, \psi(x,y+1)+\frac{m_d}{n_d}\, \psi(x,y-1)
=m_d\, n_d\, \frac{q}{\epsilon}(n-p-C)
\end{multline}
\end{document}
\cdotfor a multiplication dot. – Jun 15 '15 at 07:43