Go: cannot find package "fmt" error

Unset GOROOT - the go tools know where they are supposed to be and you rarely need to set it.

You've set it to /home/user/go and unless you build go in there that is unlikely to be the right place to find the fmt package.

Don't use apt-get for installing go, just download the binaries and extract them to your home (or any) directory.

To get the go tool available in your terminal, you have to add the export PATH=$PATH:$GOROOT/bin line to your ~/.bashrc.