Wagons and cranes

The same cranes are unloading 96 wagons.
There would be fewer wagons for each crane if there were two more cranes.
How many cranes were there?

Correct answer:

n =  4

Step-by-step explanation:

nv = 96 (n+2)(v8) = 96 nv +2v 8n  16 = 96 96 +2 96/n8n  16 = 96 2 968n216n=0  2 968n216n=0 8n216n+192=0 8n2+16n192=0 8=23 16=24 192=263 GCD(8,16,192)=23=8  n2+2n24=0  a=1;b=2;c=24 D=b24ac=2241(24)=100 D>0  n1,2=2ab±D=22±100 n1,2=22±10 n1,2=1±5 n1=4 n2=6 n>0 n=n1=4 v1=96/n=96/4=24 v2=96/(n+2)=96/(4+2)=16 n=4

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