A straight line L through the point  $(3,-2)$is inclined at an angle $60°$  to the line $\sqrt{3}x+y=1.$ If $L$ If L also intersects the x-axis, then the equation of $L$is

Let the slope of $L$ be$m$

then,  $\left|\frac{m+\sqrt{3}}{1-\sqrt{3m}}\right|=\tan {60}^{\circ }=\sqrt{3}$

$\Rightarrow m+\sqrt{3}=\sqrt{3}(1-\sqrt{3}m)$

or  $m+\sqrt{3}=-\sqrt{3}(1-\sqrt{3}m)$

$\Rightarrow m=0$ or $n=\sqrt{3}$

 But $n\ne 0$ as $L$ intersects $x$- axis 

Hence equation of L is 

$y+2=\sqrt{3}(x-3)$

or  $y-\sqrt{3}x+2+3\sqrt{3}=0$