The Exotic Burst Quad Launcher is a new addition to Fortnite, introduced in Chapter 2 Season 5 Week 10. Like all the other Exotics, this can be purchased in the game from a specific NPC that you will need to track down.
The Burst Quad Launcher fires four rockets but has a long reload time of 5.4 seconds. The magazine size is four, so you can fire once, then reload. It will do 42 damage to a player with each rocket, so is an easy enough kill on unshielded players thanks to the area of effect damage caused by the explosion of each rocket.
To get the Burst Quad Launcher, you will need to track down Fishstick in the game. He has two potential spawning areas which we will mark on the map below.
Fishstick can spawn at Coral Castle or Craggy Cliffs. At Coral Castle, he can spawn just about anywhere around the main castle area itself, while at Craggy Cliffs he will spawn in the restaurant overlooking the sea.
600 Gold Bars is how much it will set you back to get your hands on this weapon, so you will need to decide for yourself if it is worth the price. It uses standard rocket ammo, so you should be able to gather up enough to cause people some serious issues in your game.
Keep in mind, if you miss your shot because rockets are reasonably slow-moving in the game, you are going to get out damaged by just about any other weapon in the game, so it can be best to fire your rockets then instantly switch to another weapon and engage with that as well.