Da equação, temos:$$2\cdot \sin x \cdot \cos x \space =\space -\frac{\sqrt 3}{2}$$$$\sin(2x) = \sin \left(\frac{4\pi}{3} + 2\cdot k \cdot \pi \right) \implies \boxed{x = \frac{2\pi}{3} + k \cdot \pi}$$$$\text{ou}$$$$\sin(2x) = \sin \left(\frac{5\pi}{3} + 2\cdot k \cdot \pi \right) \implies x = \frac{5\pi}{6} + k \cdot \pi$$ $$\text{Alternativa } \mathbb{(A)}$$