(k-1/k)=(1/6k)+(5/3)

Solution for (k-1/k)=(1/6k)+(5/3) equation:

D( k )

k = 0

k = 0

k = 0

k in (-oo:0) U (0:+oo)

k-(1/k) = (1/6)*k+5/3 // - (1/6)*k+5/3

k-((1/6)*k)-(1/k)-(5/3) = 0

k+(-1/6)*k-k^-1-5/3 = 0

5/6*k^1-1*k^-1-5/3*k^0 = 0

(5/6*k^2-5/3*k^1-1*k^0)/(k^1) = 0 // * k^2

k^1*(5/6*k^2-5/3*k^1-1*k^0) = 0

k^1

(5/6)*k^2+(-5/3)*k-1 = 0

(5/6)*k^2+(-5/3)*k-1 = 0

DELTA = (-5/3)^2-(-1*4*(5/6))

DELTA = 55/9

DELTA > 0

k = ((55/9)^(1/2)-(-5/3))/(2*(5/6)) or k = (-(-5/3)-(55/9)^(1/2))/(2*(5/6))

k = 3/5*((55/9)^(1/2)+5/3) or k = 3/5*(5/3-(55/9)^(1/2))

k in { 3/5*(5/3-(55/9)^(1/2)), 3/5*((55/9)^(1/2)+5/3)} 

k in { 3/5*(5/3-(55/9)^(1/2)), 3/5*((55/9)^(1/2)+5/3) }