5k^2-4k-1/5k^2=16k

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Solution for 5k^2-4k-1/5k^2=16k equation: 


k in (-oo:+oo)

5*k^2-((1/5)*k^2)-(4*k) = 16*k // - 16*k

5*k^2-((1/5)*k^2)-(4*k)-(16*k) = 0

5*k^2+(-1/5)*k^2-4*k-16*k = 0

24/5*k^2-20*k = 0

DELTA = (-20)^2-(0*4*24/5)

DELTA = 400

DELTA > 0

k = (400^(1/2)+20)/(2*24/5) or k = (20-400^(1/2))/(2*24/5)

k = 25/6 or k = 0

k in { 0, 25/6 }

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