\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3x}{2}-1=arcsin\left(\dfrac{1}{4}\right)+k2\pi\\\dfrac{3x}{2}-1=\pi-arcsin\left(\dfrac{1}{4}\right)+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3x}{2}=1+arcsin\left(\dfrac{1}{4}\right)+k2\pi\\\dfrac{3x}{2}=1+\pi-arcsin\left(\dfrac{1}{4}\right)+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}+\dfrac{2}{3}arcsin\left(\dfrac{1}{4}\right)+\dfrac{k4\pi}{3}\\x=\dfrac{2}{3}+\dfrac{2\pi}{3}-\dfrac{2}{3}arcsin\left(\dfrac{1}{4}\right)+\dfrac{k4\pi}{3}\end{matrix}\right.\)
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