Once you've completed a few Campaign Missions in The Edge of Fate, the Destiny 2 Dark Academia Quest will pop up in Augur’s Bethel. You'll want to fast travel to the Curtilage Divide and follow the marker on the map down through the tunnel. Just be sure to mark Dark Academia to avoid wasting time going in circles.
After a bit of light footwork, you'll find yourself in an area infected with Fallen. Continue along the tunnel until you reach a door with a generator next to it, which has a barrier around it. Your goal will be to render the barrier useless, giving you access to the door.
Here's how you can unlock the door Destiny 2 Dark Academia quest.
How to unlock the door in the Destiny 2 Dark Academia Quest
To unlock the door in the Destiny 2 Dark Academia quest, find and shoot three batteries (or whatever they are called; look for glowing things). The first one is in plain sight, while the other two are tucked away behind panels and pipes. Here's how to go about locating and shooting these batteries.
First battery location in the Destiny 2 Dark Academia quest

The first battery location is rather straightforward. Keeping the door straight ahead, turn around and get under the stairway that leads to the door itself. The charge will be inside a vent. Alternatively, you could shoot it from atop the ramp.
Second battery location in the Destiny 2 Dark Academia quest

For the second battery, once again, turn around after facing the locked door, and head left. Look for a large pipe that's on a slant. Jump atop the ramp and turn right. While along the ramp, look to the right side, you'll see a line of pipes running flush against the wall.

Jump atop and follow it until the end, where you'll be able to Charge Matter Realignment. Interact with it and head back along the pipe until you reach the ramp once again.

Get onto the ramp, turn right, and you will be the second charge a short distance away. Destroy the covering and then shoot the battery. The last one is close by as well.
Third battery location in the Destiny 2 Dark Academia quest

After destroying the second battery, turn around on the ramp and begin descending. On your right, you'll spot a metal panel that can be destroyed to reveal a battery. Break it open and shoot the battery to overcharge the barrier.
Once you destroy all three batteries, head back to the locked door, use Matterspark, and zap the generator until it overcharges. Once it sparks, you'll know the door is open, and you'll be able to proceed with the Destiny 2 Dark Academia quest. On a side note, if this seems a bit difficult, you must not have completed the Calculus Campaign Mission, which is quite eyewatering, especially the combat.
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