My guitar has a fixed bridge setup , and i want to install Floyd Rose on it .
Can it be done without suffering any problems like loss of sustain ,bad sound quality , or breaking of wood ?
Yeah but it would be a few hundred dollars cause you would prolly have to route the body if you want to be able to pull up.
Ibanez RG7321
Jackson Randy Rhoads V with Floyd Rose
Peavey Valveking 112
Digitech RP70 Guitar Processor
It would be INSANELY expensive. What type of wood is your guitar? If it's a first act from Wally world you'll destroy it.

More than likely there's a lot more to putting one in than you think. Not only will you have to buy the system, but you'll have to route out the entire back of your guitar, make sure everything is almost perfect about the back cavity, then replace your nut.

TBH it's easier/normally cheaper to just BUY a guitar with an FR already on it. I asked a local guy if he could do it and his price (which is normally very good) was about $500, just to install it. I'd have to supply the actual unit. That's about $700, minus any extra expenses.

If you MUST have a trem on THAT guitar, go Kahler. They can be mounted on most guitars with only very little routing on top. And BTW, you're going to suffer sustain loss if you put on ANY sort of tremolo.

I love tremolo's but they have a LOT of flaws, and you do have to keep up with them or they'll go to **** fast. They're like the exotic sports cars of guitar world. Don't change the oil every 100 miles? Well then it's not going to perform.
Tossing in a Foyd on a fixed bridge guitar is a huge project. You have to route the front and back of the guitar, the Floyd going to cost you if you go for an OFR and not much less if you get a LFR.

Looking at your ESP guitar I see it's a string thru so putting the Stetsbar on it might be out as well. You might want to look into a Kahler but your still going to have to have some top routing done and a Kahler will run you over 2 hundred bucks USD.

All in all you might be better off buying a new guitar with a Floyd.

you'll need a router to route out the cavity.

honestly it will probably save you money to sell your guitar and buy one with it in it already.

what kind of guitar do you have?
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its an ESP LTD AX-50

these r d spec of my guitar :

25.5” Scale
Basswood Body
Mahogany Neck
Rosewood Fingerboard
42mm Standard Nut
Thin U Neck Contour
24 XJ Frets
Chrome Hardware
ESP Tuners
TOM Bridge
ESP LH-150 (N) LH-301 p.u.
Finish: SS
routing is half of it u have to measure out the scale redrill the holes for the floyd rose posts. 1st make sure the neck has no angle away from the body if its angled a little give up now cause its hell to fix that. Then figure out what size of floyd u need yes there are different sizes and u get the wrong one ull ruin ur guitar. measure everything a dozen or so times and make sure its perfect for scale and straight and level And then u gotta make a hole where the block is gonna go through once u have that route out the back a little bit for the springs u gotta do it right so the springs dont rub and kill ur sound. then u gotta drill the holes for hte posts the best way i found is actually drill em into some dowling then pound the dowling into some big holes on ur guitar for the best effect. then the locking nut. point ur old nut out. set the new net perfectly either by carving it deeper or setting up a system to raise it. u can actually buy wedges to do it. then drill it in and it will all be awesome. but it could also be a collosal failure u just gotta try and and see i guess and by that i mean forget about and buy a new guitar with a floyd rose
Keep On Keepen' On
Your gonna lose sustain going from fixed to FR just the way things are. And as your guitar is 219$ new a good FR and installation is going to cost almost double what the guitar cost. Way more economical to buy a good guitar with a FR. If the ESP is your only guitar you could be without a guitar for a while getting the FR put in.