x-2/3=1/x

Solution for x-2/3=1/x equation:

D( x )

x = 0

x = 0

x = 0

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

x-(2/3) = 1/x // - 1/x

x-(1/x)-(2/3) = 0

x-x^-1-2/3 = 0

1*x^1-1*x^-1-2/3*x^0 = 0

(1*x^2-2/3*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-2/3*x^1-1*x^0) = 0

x^1

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

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

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

DELTA = 40/9

DELTA > 0

x = ((40/9)^(1/2)-(-2/3))/(1*2) or x = (-(-2/3)-(40/9)^(1/2))/(1*2)

x = ((40/9)^(1/2)+2/3)/2 or x = (2/3-(40/9)^(1/2))/2

x in { (2/3-(40/9)^(1/2))/2, ((40/9)^(1/2)+2/3)/2} 

x in { (2/3-(40/9)^(1/2))/2, ((40/9)^(1/2)+2/3)/2 }