1/8=k-10/k

Solution for 1/8=k-10/k equation:

D( k )

k = 0

k = 0

k = 0

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

1/8 = k-(10/k) // - k-(10/k)

10/k-k+1/8 = 0

10*k^-1-1*k^1+1/8*k^0 = 0

(1/8*k^1-1*k^2+10*k^0)/(k^1) = 0 // * k^2

k^1*(1/8*k^1-1*k^2+10*k^0) = 0

k^1

(1/8)*k-k^2+10 = 0

(1/8)*k-k^2+10 = 0

DELTA = (1/8)^2-(-1*4*10)

DELTA = 2561/64

DELTA > 0

k = ((2561/64)^(1/2)-(1/8))/(-1*2) or k = (-(1/8)-(2561/64)^(1/2))/(-1*2)

k = ((2561/64)^(1/2)-1/8)/(-2) or k = ((2561/64)^(1/2)+1/8)/2

k in { ((2561/64)^(1/2)-1/8)/(-2), ((2561/64)^(1/2)+1/8)/2} 

k in { ((2561/64)^(1/2)-1/8)/(-2), ((2561/64)^(1/2)+1/8)/2 }