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Real numbers a,b,c,da,b,c,da,b,c,d satisfy
a2+b2=c2+d2.a^2+b^2=c^2+d^2.a2+b2=c2+d2.
If the maximum of the expression
20bc+14bd+20ad−14aca2+b2+c2+d2\dfrac{20bc+14bd+20ad-14ac}{a^2+b^2+c^2+d^2}a2+b2+c2+d220bc+14bd+20ad−14ac
can be expressed as n\sqrt{n}n for some positive integer nnn, what is the value of n?n?n?
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