PatrioticPickle :
Check the dimensions of the card from the manufacturer website, then measure the inside of the case.
But I agree with the above, being a slim desktop case it probably wont fit most GPUs
Yes mine is the biggest one of the 4 in this picture
https://www.google.ie/search?q=hp+slim+desktop&espv=2&biw=1920&bih=974&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiTuOCk2_DOAhVnBsAKHe8kBMEQ_AUIBigB#tbm=isch&q=hp+desktops+compaq+elite+8300&imgrc=EoYy8AmCji6m2M%3A