6/10=k-3/k

Solution for 6/10=k-3/k equation:

D( k )

k = 0

k = 0

k = 0

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

6/10 = k-(3/k) // - k-(3/k)

3/k-k+6/10 = 0

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

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

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

k^1

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

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

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

DELTA = 309/25

DELTA > 0

k = ((309/25)^(1/2)-(3/5))/(-1*2) or k = (-(3/5)-(309/25)^(1/2))/(-1*2)

k = ((309/25)^(1/2)-3/5)/(-2) or k = ((309/25)^(1/2)+3/5)/2

k in { ((309/25)^(1/2)-3/5)/(-2), ((309/25)^(1/2)+3/5)/2} 

k in { ((309/25)^(1/2)-3/5)/(-2), ((309/25)^(1/2)+3/5)/2 }