Absolutely not compatible. You have a less than 300w psu. Optiplex computers are for business use so no movie watching or game playing. That card need a minimum of 500w psu. Also power supplies on Optiplex usually cannot be upgraded. https://www.asus.com/us/Graphics-Cards/DUAL-RX580-O8G/specifications/

See this-- https://www.dell.com/community/Desktops-General-Read-Only/OptiPlex-7020-MT-Video-Power-Upgrades/td-p/4535812

I have a spare 1200 psu do you think i can make that happen? 

7020/9020 does not use standard power supply so no.

what case is it?  why post lacking such a fact. MT, SFF 

my guess is since you said (implied ) the 1200w fits must be the BIG'N the MT minitower case

when posting assume we can see what you own. sitting there,  what case, what case? and what's inside it now matters,too.

it is Q87 based and Pentium (4th gen/Haswell) 

not chopped liver in that regard.

THE MT IN FACT DOES USE  A NEAR, ATX SIZED PSU. BUT NEEDS AND ADAPTOR

NOTE THE 24 PIN CONNECTOR MISSING? YET?

NOTE THE 12VDC ONLY CABLES>? OPPS.

And gutless 290watts (if that is it)

what sizes PSU do you need, 700watts up is best, for fast GPU, are you doing fast GPU?

the stock rails 12v are 14/16a, so easy .

note the lack of 24 pins below on the MT.  4pin and 8pin only there, look on yours yet, seems not.

no 24pins here, see?

google DELL , psu adapter 24p to 8pin

bingo

here a real case 7020 MT

when exceeding 700watt the PSU gets longer, (how else?) must fit into (transgress) to this space here.

what is do use use a ruler, and measure the space, first. or OGM  rip out DVD cages note needed.
even to the point of drilling out POP-rivets seen there, (using vacuum cleaner with hand 2, to catch filings)

7020MT

IF this is an SFF PC, ill delete my post,  but no PC stated yet and is 1st.

cases MATTER ! I rest my CASE.

Does not matter which size it is.

7020/9020 DOES NOT USE standard power supply connectors.

USFF SFF DT MT

You will have to upgrade the psu and also buy a 24 pin to 8 pin adapter for the motherboard but other than that you should be fine

Eso sí hay que comprarle una fuente adicional para Gamer y deber ser la cpu TM no la la mini. 

Si en la actualidad está cpu soporta esa tarjeta gráfica yo personal mente tengo 2 montada en esta PC. Lo único que no se es cuántas más podría montar.

I have an Optiplex 7020 MT and All I need what a Power Adapter 24 pin to 8 pin. amazon sells them and so doesnt ebay. Easy Upgrade