$sin\Bigg(2x-30°\Bigg)=\dfrac{\sqrt{2}}{2}$
$⇔sin\Bigg(2x-30°\Bigg)=sin45°$
$⇔\left[ \begin{array}{l}2x-30°=45°+360°k\\2x-30°=180°-45°+360°k\end{array} \right.$ 
$⇔\left[ \begin{array}{l}x=37,5°+180°k\\x=82,5°+180°k\end{array} \right.(k∈\mathbb{Z})$ 
Chúc bạn học tốt!