How to break a long equation?

Use split environment provided by amsmath package.

\begin{equation}
\begin{split}
F = \{F_{x} \in  F_{c} &: (|S| > |C|) \\
 &\quad \cap (\text{minPixels}  < |S| < \text{maxPixels}) \\
 &\quad \cap (|S_{\text{conected}}| > |S| - \epsilon) \}
\end{split}
\end{equation}

The aligned environment from amsmath is also a good option:

\begin{equation}
\begin{aligned}
F ={} & \{F_{x} \in  F_{c} : (|S| > |C|) \\
      & \cap (\mathrm{minPixels}  < |S| < \mathrm{maxPixels}) \\
      & \cap (|S_{\mathrm{conected}}| > |S| - \epsilon)\}
\end{aligned}
\end{equation}

For simple multi-line equations without alignment, use the multline environment:

\begin{multline}
F = \{F_{x} \in  F_{c} : (|S| > |C|) \cap 
(minPixels  < |S| < maxPixels) \\ \cap 
(|S_{conected}| > |S| - \epsilon)
  \}
\end{multline}