After installing Java 8 manually, since the .deb file wouldn't install otherwhise, I had the launcher installed, using the .deb file. But in my installed Apps the launcher had no icon and when trying to start it nothing happend. Trying to start it using the terminal showed these "error"-Messages:

minecraft-launcher: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by minecraft-launcher)
minecraft-launcher: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `CXXABI_1.3.9' not found (required by minecraft-launcher)
minecraft-launcher: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.21' not found (required by minecraft-launcher)

Right now I am working around this issue, by using the leagcy version of the Minecraft-Launcher which I found a working launcher.jar file of in the internet(not on the offial site, which is a bummer)

And I have to use Ubuntu 14.04, because for newer versions there is no graphics driver avalable anymore for my hardware.