1/2k+2/k+4=5/k

Solution for 1/2k+2/k+4=5/k equation:

D( k )

k = 0

k = 0

k = 0

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

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

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

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

1/2*k^1-3*k^-1+4*k^0 = 0

(1/2*k^2+4*k^1-3*k^0)/(k^1) = 0 // * k^2

k^1*(1/2*k^2+4*k^1-3*k^0) = 0

k^1

(1/2)*k^2+4*k-3 = 0

(1/2)*k^2+4*k-3 = 0

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

DELTA = 22

DELTA > 0

k = (22^(1/2)-4)/(2*(1/2)) or k = (-22^(1/2)-4)/(2*(1/2))

k = 22^(1/2)-4 or k = -(22^(1/2)+4)

k in { -(22^(1/2)+4), 22^(1/2)-4} 

k in { -(22^(1/2)+4), 22^(1/2)-4 }