Chọn phương án A.

\(\begin{aligned}
2\sin\left(\dfrac{x}{2}+30^\circ\right)-1=0\Leftrightarrow&\sin\left(\dfrac{x}{2}+30^\circ\right)=\dfrac{1}{2}\\
\Leftrightarrow&\left[\begin{array}{l}\dfrac{x}{2}+30^\circ=30^\circ+k360^\circ\\ \dfrac{x}{2}+30^\circ=150^\circ+k360^\circ\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}\dfrac{x}{2}=k360^\circ\\ \dfrac{x}{2}=120^\circ+k360^\circ\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}x=k720^\circ\\ x=240^\circ+k720^\circ\end{array}\right.\,\left(k\in\mathbb{Z}\right)
\end{aligned}\)