It's here

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xrandr -q
Screen 0: minimum 320 x 200, current 5685 x 1800, maximum 16384 x 16384
eDP-1 connected primary 3200x1800+2485+0 (normal left inverted right x axis y axis) 293mm x 165mm
   3200x1800     60.00*+  59.96    59.94    48.00 
   2880x1620     59.96    59.97 
   2560x1600     59.99    59.97 
   2560x1440     59.99    59.99    59.96    59.95 
   2048x1536     60.00 
   1920x1440     60.00 
   1856x1392     60.01 
   1792x1344     60.01 
   2048x1152     59.99    59.98    59.90    59.91 
   1920x1200     59.88    59.95 
   1920x1080     60.01    59.97    59.96    59.93 
   1600x1200     60.00 
   1680x1050     59.95    59.88 
   1600x1024     60.17 
   1400x1050     59.98 
   1600x900      59.99    59.94    59.95    59.82 
   1280x1024     60.02 
   1440x900      59.89 
   1400x900      59.96    59.88 
   1280x960      60.00 
   1440x810      60.00    59.97 
   1368x768      59.88    59.85 
   1360x768      59.80    59.96 
   1280x800      59.99    59.97    59.81    59.91 
   1152x864      60.00 
   1280x720      60.00    59.99    59.86    59.74 
   1024x768      60.04    60.00 
   960x720       60.00 
   928x696       60.05 
   896x672       60.01 
   1024x576      59.95    59.96    59.90    59.82 
   960x600       59.93    60.00 
   960x540       59.96    59.99    59.63    59.82 
   800x600       60.00    60.32    56.25 
   840x525       60.01    59.88 
   864x486       59.92    59.57 
   800x512       60.17 
   700x525       59.98 
   800x450       59.95    59.82 
   640x512       60.02 
   720x450       59.89 
   700x450       59.96    59.88 
   640x480       60.00    59.94 
   720x405       59.51    58.99 
   684x384       59.88    59.85 
   680x384       59.80    59.96 
   640x400       59.88    59.98 
   576x432       60.06 
   640x360       59.86    59.83    59.84    59.32 
   512x384       60.00 
   512x288       60.00    59.92 
   480x270       59.63    59.82 
   400x300       60.32    56.34 
   432x243       59.92    59.57 
   320x240       60.05 
   360x202       59.51    59.13 
   320x180       59.84    59.32 
DP-1 disconnected (normal left inverted right x axis y axis)
HDMI-1 disconnected (normal left inverted right x axis y axis)
HDMI-2 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 521mm x 293mm
   1920x1080     60.00*+  50.00    59.94    30.00    25.00    24.00    29.97    23.98 
   1920x1080i    60.00    50.00    59.94 
   1680x1050     59.88 
   1280x1024     75.02    60.02 
   1280x720      60.00    50.00    59.94 
   1024x768      75.03    60.00 
   800x600       75.00    60.32    56.25 
   720x576       50.00 
   720x576i      50.00 
   720x480       60.00    59.94 
   720x480i      60.00    59.94 
   640x480       75.00    72.81    66.67    60.00    59.94 
   720x400       70.08

oguzkarayemis wrote:

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xrandr -q
Screen 0: minimum 320 x 200, current 5685 x 1800, maximum 16384 x 16384
eDP-1 connected primary 3200x1800+2485+0 (normal left inverted right x axis y axis) 293mm x 165mm
…
HDMI-2 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 521mm x 293mm
…


Here you can see both of your connected monitors.

So lets test following (you can replace left with right if the second display is right of your laptop)

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xrandr --output HDMI-2  --left-of eDP-1

This setting is not persistent, so if anything does not fit, you can always type in `xrandr --auto` to get back to the basic setting. You could also play around with the resolutions to find something fitting your needs.

The UbuntuWiki:X-Config-Resolution shows you some examples, but be careful with persistent configurations as it can lead you to a non working graphical desktop. On failure you can always switch over to another TTY using the default shortcuts ctrl+alt+F1 to F7 and revert the not working settings, if needed.

If you found a working setup, let us know

I found on another forums post a minimal configuration for nvidia cards using the xorg.conf:

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Section "Device"
    Identifier     "nvidia"
    Driver         "nvidia"
    VendorName     "NVIDIA Corporation"
    BusID          "…HERE…"
    Option         "AllowEmptyInitialConfiguration"
EndSection


Replace the «…HERE…» with the BusID, e.g. PCI:1:0:0

So, that's the report:
I tried every possible combination for xorg.conf, and none of them worked. It was a very sad story actually. But, tonight I upgraded my system to Kubuntu 20.10 (and KDE 19.5). Now, this problem was resolved by itself. I don't know where was the problem exactly, but I think maybe a series of communication issues between several modules. But now, everything is just ok.
Thank you all for great efforts for solving my issue.