Will this card run on my Acer aspire m3450 motherboard?

Solution
From Hardware Secrets review of the Raidmax Seiran case:

In its default configuration, the Raidmax Seiran supports video cards up to 17.3" (440 mm) long, but if you install a hard drive in front of the video card, this clearance is reduced to 9.8" (250 mm). If you move the front fan, and one of the racks that hold it is in front of the video card, you can install video cards up to 11.4" (290 mm) long.

The PowerColor 2GBD5-2DHPPV3E AMD Radeon HD 7870 2048MB GDDR5 PCIe 3.0 x16 MYST Edition Video Card is 10.5" (267 mm) in length.

The PowerColor Radeon HD 7750, that you've tested, is a PCI Express 3.0 card. Your new Radeon HD 7870 card is also a PCI Express 3.0 card so it should work fine.
From Hardware Secrets review of the Raidmax Seiran case:

In its default configuration, the Raidmax Seiran supports video cards up to 17.3" (440 mm) long, but if you install a hard drive in front of the video card, this clearance is reduced to 9.8" (250 mm). If you move the front fan, and one of the racks that hold it is in front of the video card, you can install video cards up to 11.4" (290 mm) long.

The PowerColor 2GBD5-2DHPPV3E AMD Radeon HD 7870 2048MB GDDR5 PCIe 3.0 x16 MYST Edition Video Card is 10.5" (267 mm) in length.

The PowerColor Radeon HD 7750, that you've tested, is a PCI Express 3.0 card. Your new Radeon HD 7870 card is also a PCI Express 3.0 card so it should work fine.
 
Solution