HAXM not working on Linux

HAXM is only needed on Windows and OS X. On Linux, you need to have KVM installed.

See the "Configuring VM Acceleration on Linux" section on: https://developer.android.com/studio/run/emulator-acceleration#vm-linux

Just download x86 based system images in the SDK Manager, then start the AVD, KVM will be auto-detected and used automatically if your machine/system supports it.

As already mentioned by @Digit, you do not need HAXM on Linux but KVM.

Although the links in the other answers give a comprehensive answer, for those who like it short, on my Ubuntu, this was just enough:

sudo apt-get install kvm