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\begin{align*}
	\left.\begin{array}{l}
		\sum_{}^{}F_{iH} = 0 = F-S_1 \frac{\sqrt{2}}{2} + S_3 \frac{\sqrt{2}}{2} \\
		\sum_{}^{}F_{iV} = 0 = F - S_1 \frac{\sqrt{2}}{2} -S_2-S_3\frac{\sqrt{2}}{2} \\
		\hline
	\end{array}
	\right\}
	\qquad + \\
	\begin{array}{l}
		\rightarrow S_1	= \sqrt{2} F - \frac{1}{\sqrt{2}} S_2 
	\end{array}
\end{align*}

\documentclass{scrartcl}

\usepackage{amsmath}

\begin{document}
\begin{align*} 
  &\left.\begin{array}{l} 
    \sum F_{iH} = 0 = F-S_1 \frac{\sqrt{2}}{2} + S_3 \frac{\sqrt{2}}{2} \\ 
    \sum F_{iV} = 0 = F - S_1 \frac{\sqrt{2}}{2} -S_2-S_3\frac{\sqrt{2}}{2} \\[3pt] 
  \hline 
  \end{array} \, \right\}  \qquad + \\ 
  &\hspace{\tabcolsep}\rightarrow~S_1 = \sqrt{2} F - \frac{1}{\sqrt{2}} S_2 
 \end{align*} 
\end{document}