2y-1/y=2/3

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

D( y )

y = 0

y = 0

y = 0

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

2*y-(1/y) = 2/3 // - 2/3

2*y-(1/y)-(2/3) = 0

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

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

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

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

y^1

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

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

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

DELTA = 76/9

DELTA > 0

y = ((76/9)^(1/2)-(-2/3))/(2*2) or y = (-(-2/3)-(76/9)^(1/2))/(2*2)

y = ((76/9)^(1/2)+2/3)/4 or y = (2/3-(76/9)^(1/2))/4

y in { (2/3-(76/9)^(1/2))/4, ((76/9)^(1/2)+2/3)/4} 

y in { (2/3-(76/9)^(1/2))/4, ((76/9)^(1/2)+2/3)/4 }