\(\Rightarrow\left[{}\begin{matrix}sin\left(x+\dfrac{\pi}{6}\right)=\dfrac{-3+\sqrt{17}}{4}\\sin\left(x+\dfrac{\pi}{6}\right)=\dfrac{-3-\sqrt{17}}{4}< -1\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=arcsin\left(\dfrac{-3+\sqrt{17}}{4}\right)+k2\pi\\x+\dfrac{\pi}{6}=\pi-arcsin\left(\dfrac{-3+\sqrt{17}}{4}\right)+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{6}+arcsin\left(\dfrac{-3+\sqrt{17}}{4}\right)+k2\pi\\x=\dfrac{5\pi}{6}-arcsin\left(\dfrac{-3+\sqrt{17}}{4}\right)+k2\pi\end{matrix}\right.\)
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