This can be patched, but we can't answer whether you have the skills to do it or would be happy with the outcome.
If you're willing to take it on, patching drywall cutouts like this usually involve:
- Inserting more screws to keep the patch area properly secured to any studs. Large sheets of drywall can support themselves across gaps but as you cut holes in it, the holes lose some of that stability. If this section of drywall is already well secured to studs, skip this step.
- Use drywall mud and drywall seam tape to cover the seams. Most drywall tapes are made to be embedded in mud, so you apply the mud with a wide drywall knife, add the tape, and then add more mud over the top. This helps keep flexing from causing cracks later.
- Wait for the mud to dry, then sand it. Reapply mud if needed (usually 2+ rounds of mud and sanding are necessary in fresh drywall) You're finished with mudding and sanding when the surface looks reasonably flat.
- Prime (and wait for primer to dry) then paint. Matching paint is typically harder than it's worth, it's better to paint the whole wall a complementary color.
