After the Fire Support quest, Paladin Danse will have you prove your worth by having you join him on a quest. This will lead you to ArcJet Systems west of Cambridge. The path will be easy, especially since Danse is well-armed.
Objectives within ArcJet Systems involve a short series of hitting switches and restoring power. Along the way, you'll meet a lot of Synths to fight, so be sure you've equipped the best weapons in your inventory.
As you follow Danse, you'll reach a rocket engine test firing room. You'll first have to restore power to the engine core. When you reach the room with the activation switch, head to the back of the room where you will find a terminal.Hack the terminalto restore power. Now before you activate the engine, help Danse clear out the Synths that have filled the engine room. When you activate the engine, stay where you are until the test firing is complete.
Now that the elevator is operational, take it up to the control room. Clear out the room of Synths and grab the main objective of the quest, the Deep Range Transmitter. Then leave ArcJet Systems. A conversation with Paladin Danse will complete the quest, after which he will ask you to join the Brotherhood.