At startup the monitor that doesn't get detected after logging in displays the startup console.
I have been trying to fix this for a few days.

Incase you need it:
xrandr

What desktop environment are you running?

kudos for providing command output in your first post!

but...
how?
more output please.

also:
and info about the monitors.

does nothing for me.

Output for lspci -k | grep -iEA5 'vga|3d|display'

output for: uname -rv
When I was trying to fix it myself first, I tried installing the nvidia drivers, and might have done something else aswell. I don't recall,
but afterwards I rebooted and my monitors would not display the desktop at all anymore.

I am running LXQT on debian 9

Output for: lspci -k | grep -iEA5 'vga|3d|display'

Output for: uname -rv
I am going to guess as to what info about the monitors you need,
The left monitor is completely black after logging in. (Acer) doesn't get detected.
The right monitor is just fine. (Medion) gets detected

You can set up your displays in gnome-control-center. Also, some video cards have multiple outputs, but they will only use one at a time. What is the startup console?

Xrandr is showing only 1 output. So, X thinks there is only one possible display. I've never seen that before. Onboard video usually will use only one output at a time.

Trying to use onboard video together with a video card for multiple displays seldom produces the desired result unless the mobo is designed for that.

is not the same as
computers are like that, pedantic to a fault.

anyhow, thanks for providing output again.
i forgot to ask one important question:
Is this a laptop?

because if it is, you have a so-called "hybrid graphics" setup which requires
a) the proprietary nvidia driver and
b) some special software - it used to be bumblebee, but has been replaced by something else (optimus?) afaik.

if it isn't, then this is a rather complex matter of
a) where you are actually plugging the monitors in
b) getting the X server to recognize and use BOTH cards - all i can say is i tried this at some point, in maybe three different ways, failed, gave up.

No, it is not a laptop. It is a desktop, the working monitor is plugged into HDMI, and the other one is VGA.
I know it is possible, on Ubuntu it detected them by default.

Someone suggested me to download Ubuntu Server and install LXQT, but I have no idea what he means exactly.
But apparently it would detect both monitors that way?

I doubt that(*), but if Ubuntu is ok for you, well just use it!

You can also use Lubuntu or Xubuntu /different desktop environments), or you can install a non-graphical ubuntu and build your own customised desktop.

(*) This is a highly specialised setup and I don't see how it can be automated. research into debian wiki & various forums etc. is necessary which you have shown no proof of...

Well, it is difficult for us to determine what you might have done. And if it was the cause of your monitors not working properly anymore, you may be better off reinstalling.

In most cases I have personally experienced, monitors were detected automatically. When they were not, I used to detect it, this duplicated the displays on attached monitors, I then ran a command such as the following to extend the display, rather than duplicate it Also, as AwesomeMachine mentioned If you have not already, try another cable for your display.

Try a different kernel. I've got 3 monitors and some kernels won't light them all up. You've probably got 4.10.1 or 4.10.5 available to you.