dontlistentome :
You'd use the pci-ex x16 slot for the videocard, the x4 slot is for other pci-ex devices you might use, such as a wi fi card. So with a dual slot card you'll lose access to that slot. A 1050 is a good choice for that computer.
Sorry mate, bad news - this is CRAPPY BTX FORMAT - look at pictures below.
So, which one of PCIE x16 slots is wired as X4, I am suspecting the White one, if it is, you can instal only Single Bracket video card into PCIE x16 (wired as x16) Black Slot.
In this case you are limited to GT 1030, because GTX 1050 and above uses double bracket..
The only way around it is to find GTX 1050 or GTX 1050TI card where there is no connectors on the one side of the bracket.
Let me try to explain.
You would have to disassemble the card and remove Dual Bracket, then use metal saw and cut bracket along the line, assemble card back - and now you have GTX 1050 TI single bracket.
Next, you might have to change case exhaust fan for something more skinnier, because GPU fan shroud might push against exhaust fan.
Or we need to find GTX 1050 (or TI) with different, more skinnier (at the bracket) shroud.
If you ready to do all this, I will start looking for more appropriate GTX 1050 TI model.
If you don't want to do all this cutting and fitting, the only option is GT 1030.
What is your choice?