$35sinx- \sqrt{3} scosx=50 \Rightarrow \frac{35sinx- 35\sqrt{3} cos}{70} = \frac{50}{70} $
$sinx. \frac{1}{2} - \frac{ \sqrt{3} }{2} cosx= \frac{5}{7} \Rightarrow sinx.cos \frac{ \pi }{3}-cosx.sin \frac{ \pi }{3}=\frac{5}{7}$
$sin(x-\frac{ \pi }{3})=\frac{5}{7}$
$ \Rightarrow x-\frac{ \pi }{3}=2k \pi +sin^{-1}(\frac{5}{7}),x-\frac{ \pi }{3}=2(k+1)\pi -sin^{-1}(\frac{5}{7})$
$ \Box $
