# Find all solutions of the equation in the interval [ 0 , 2 <mrow class="MJX-TeXAtom-

Find all solutions of the equation in the interval $\left[0,2\pi \right)$: $7{\mathrm{sec}}^{2}\left(x\right)-7\mathrm{sec}\left(x\right)=14$
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Hugo Bruce
$7\left(\mathrm{sec}x{\right)}^{2}-7\mathrm{sec}x=14\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\left(\mathrm{sec}x{\right)}^{2}-\mathrm{sec}x-2=0$
By factoring, $\left(\mathrm{sec}x-2\right)\left(\mathrm{sec}x+1\right)=0$