I remember this error message used to happen on OpenSuSE only. For Ubuntu and Debian users, it's absolutely no problem to use "sudo gparted&" or any other commands that invoke a GUI program with other UID. However in Debian 8(Jessie), this issue occurs:
(gpartedbin:13344): Gtk-WARNING **: cannot open display: :0
I used to try sudo gksu/kdesudo to solve this issue, but still in vain, apparently this doesn't hit the point.
After checking many Debian guru's advices, I believe below is the correct solution to this issue. Please append one line in /etc/sudoers:
Defaults env_keep+="DISPLAY HOME"No need to login, your linux can now launch GUI programs with other UIDs.