Answer
$x+2y+z=5$
Work Step by Step
Mid-point of points $(3,4,0)$ and $(1,0,-2)$ is $M=(2,2,-1)$
Normal vector: $n=\lt 1,2,1\gt $
Transform $M$ into vector form as: $M=\lt x-2, y-2,z+1\gt $
$n \cdot M= \lt 1,2,1\gt \cdot \lt x-2, y-2,z+1\gt =0 $
$1(x-2)+2( y-2)+1(z+1)=0 $
Hence, the equation of the plane is:
$x+2y+z=5$