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

Solution for 2(1/x)^2-(1/x)^1-1=0 equation:

D( x )

x = 0

x = 0

x = 0

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

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

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

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

t_1 = x^-1

2*t_1^2-1*t_1^1-1 = 0

2*t_1^2-t_1-1 = 0

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

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+1)/(2*2) or t_1 = (1-9^(1/2))/(2*2)

t_1 = 1 or t_1 = -1/2

t_1 = -1/2

x^-1+1/2 = 0

1*x^-1 = -1/2 // : 1

x^-1 = -1/2

-1 < 0

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

1 = -1/2*x^1 // : -1/2

-2 = x^1

x = -2

t_1 = 1

x^-1-1 = 0

1*x^-1 = 1 // : 1

x^-1 = 1

-1 < 0

1/(x^1) = 1 // * x^1

1 = 1*x^1 // : 1

1 = x^1

x = 1

x in { -2, 1 }