How network load-balancers work?

when large request coming to the dmz network the load balancer manage the request for1st server50 requests and2nd server50 request and similary 

You need to be specific and accurate in asking questions, in what area are you pointing to "load-balance" !

Load balancing work on two basis :

Per-Destination : the packets  sent for a two specific  destinations   go over a two specific paths.

Per-packet : the packets for the same destination can take different paths to that destination. 

For process-switching : Load balancing in on a per-packet basis.

For fast-switching : Load balancing is on per-destination basis.

By default fast-switching is enabled under Cisco interfaces

to set per-packet load balancing :

# conf t

# interface Ethernet0

# no ip route-cache

In short -  Load Balancer  are making equal routing metrics, these equal routes get installed in the routing table, and they get used equally.

Greetings Majid,Kindly note that the routers could be Load-Balancers, they way they work is when there are equal routing metrics, these equal routes get installed in the routing table, and they get used equally.The Routing protocol EIGRP has an advantage of UNequal load balancing, for example, it could use two links1:2 and we would do that if we have a link double the speed of the other link.Hope my answer satisfied your question, and I would be glad to provide additional clarifications if required.Thanks