Code: Select all
\documentclass[12pt]{article}
\usepackage[total={6.25in,10in},left=1.25in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{mathtools}
\newcommand*{\1}{\hspace{1pt}}
\newcommand*{\tsqrt}[1]{{\textstyle{\sqrt{#1}}}}
\begin{document}
Test :
\begin{flalign}
\mathrlap{\text{if $4 \, \omega_0^2 > \gamma^2$ :}} && \lambda &= \frac{1}{2} \1 \tsqrt{\displaystyle{4 \, \omega_0^2 - \gamma^2}}, & \\[12pt]
\mathrlap{\text{if $4 \, \omega_0^2 < \gamma^2$ :}} && \kappa &= \frac{1}{2} \1 \tsqrt{\displaystyle{\gamma^2 - 4 \, \omega_0^2}}. &
\end{flalign}
\begin{equation}
EQUATION
\end{equation}
\end{document}