2sin^2x + căn3 sin 2x – 2(căn3 sinx + cosx) -7 =0

$\begin{array}{l}
2{\sin ^2}x + \sqrt 3 \sin 2x – 2\left( {\sqrt 3 \sin x + \cos x} \right) – 7 = 0\,\,\left( * \right)\\
Dat\,\sqrt 3 \sin x + \cos x = t\left( { – 2 \le t \le 2} \right)\,thi:\\
{t^2} = 3{\sin ^2}x + 2\sqrt 3 \sin x\cos x + {\cos ^2}x = 2{\sin ^2}x + \sqrt 3 \sin 2x + 1\\
\Rightarrow 2{\sin ^2}x + \sqrt 3 \sin 2x = {t^2} – 1\\
\Rightarrow \left( * \right) \Leftrightarrow {t^2} – 1 – 2t – 7 = 0 \Leftrightarrow {t^2} – 2t – 8 = 0 \Leftrightarrow \left[ \begin{array}{l}
t = – 2\left( {TM} \right)\\
t = 4\left( {loai} \right)
\end{array} \right.\\
\Rightarrow \sqrt 3 \sin x + \cos x = – 2 \Leftrightarrow \frac{{\sqrt 3 }}{2}\sin x + \frac{1}{2}\cos x = – 1\\
\Leftrightarrow \sin \left( {x + \frac{\pi }{6}} \right) = \sin \left( { – \frac{\pi }{2}} \right) \Leftrightarrow x + \frac{\pi }{6} = – \frac{\pi }{2} + k2\pi \Leftrightarrow x = – \frac{{2\pi }}{3} + k2\pi
\end{array}$