Complex Conjugate intersections with axis

$$(2-i)z + (2+i)\overline{z} = 20.$$ Where does this intersect the real axis? Currently, I am thinking of going into the format of az+b$$\overline{z}$$ but I don't think this will bring me anywhere. Any ideas?

If $$z$$ is real, then $$z = \overline{z}$$ and the equation becomes $$(2+i)z + (2-i)z = 20,$$ i.e., $$4z = 20.$$
Hence the intersection with the real axis is $$z = 5$$.