x-5/x=5/9

Solution for x-5/x=5/9 equation:

D( x )

x = 0

x = 0

x = 0

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

x-(5/x) = 5/9 // - 5/9

x-(5/x)-(5/9) = 0

x-5*x^-1-5/9 = 0

1*x^1-5*x^-1-5/9*x^0 = 0

(1*x^2-5/9*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-5/9*x^1-5*x^0) = 0

x^1

x^2+(-5/9)*x-5 = 0

x^2+(-5/9)*x-5 = 0

DELTA = (-5/9)^2-(-5*1*4)

DELTA = 1645/81

DELTA > 0

x = ((1645/81)^(1/2)-(-5/9))/(1*2) or x = (-(-5/9)-(1645/81)^(1/2))/(1*2)

x = ((1645/81)^(1/2)+5/9)/2 or x = (5/9-(1645/81)^(1/2))/2

x in { (5/9-(1645/81)^(1/2))/2, ((1645/81)^(1/2)+5/9)/2} 

x in { (5/9-(1645/81)^(1/2))/2, ((1645/81)^(1/2)+5/9)/2 }