\(2cos\left(x+\dfrac{\pi}{6}\right)-1=0\Rightarrow cos\left(x+\dfrac{\pi}{6}\right)=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=\dfrac{\pi}{3}+k2\pi\\x+\dfrac{\pi}{6}=-\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Rightarrow x=\left\{-\dfrac{\pi}{2};\dfrac{\pi}{6};\dfrac{3\pi}{2}\right\}\Rightarrow-\dfrac{\pi}{2}+\dfrac{\pi}{6}+\dfrac{3\pi}{2}=\dfrac{7\pi}{6}\)