Wagons and cranes

Several of the same cranes unloaded 96 wagons.
If there were 2 more cranes there would be less 8 wagons for each crane.
How many cranes were here?

Correct result:

n =  4

Solution:

nv=96 (n+2)(v8)=96 nv+2v8n16=96 96+2 96/n8n16=96 2968n216n=0  2 968n216n=0 8n216n+192=0 8n2+16n192=0  a=8;b=16;c=192 D=b24ac=16248(192)=6400 D>0  n1,2=b±D2a=16±640016 n1,2=16±8016 n1,2=1±5 n1=4 n2=6   Factored form of the equation:  8(n4)(n+6)=0 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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