\(\Leftrightarrow6\cdot\dfrac{1-cos2x}{2}+7\sqrt{3}sin2x-8\cdot\dfrac{1+cos2x}{2}=6\)
\(\Leftrightarrow3-3cos2x+7\sqrt{3}sin2x-4-4cos2x=6\)
\(\Leftrightarrow7\sqrt{3}\cdot sin2x-7cos2x=6+4-3=7\)
\(\Leftrightarrow\sqrt{3}\cdot sin2x-cos2x=1\)
\(\Leftrightarrow2\cdot\sin\left(2x-\dfrac{\Pi}{6}\right)=1\)
\(\Leftrightarrow\sin\left(2x-\dfrac{\Pi}{6}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\Pi}{6}=\dfrac{\Pi}{6}+k2\Pi\\2x-\dfrac{\Pi}{6}=\dfrac{5}{6}\Pi+k2\Pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\left(\dfrac{\Pi}{3}+k2\Pi\right)\\x=\dfrac{1}{2}\left(\Pi+k2\Pi\right)\end{matrix}\right.\)
