1/x^2-9/x+20=0

Solution for 1/x^2-9/x+20=0 equation:

D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/(x^2)-(9/x)+20 = 0

1/(x^2)-9*x^-1+20 = 0

x^-2-9*x^-1+20 = 0

t_1 = x^-1

1*t_1^2-9*t_1^1+20 = 0

t_1^2-9*t_1+20 = 0

DELTA = (-9)^2-(1*4*20)

DELTA = 1

DELTA > 0

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

t_1 = 5 or t_1 = 4

t_1 = 4

x^-1-4 = 0

1*x^-1 = 4 // : 1

x^-1 = 4

-1 < 0

1/(x^1) = 4 // * x^1

1 = 4*x^1 // : 4

1/4 = x^1

x = 1/4

t_1 = 5

x^-1-5 = 0

1*x^-1 = 5 // : 1

x^-1 = 5

-1 < 0

1/(x^1) = 5 // * x^1

1 = 5*x^1 // : 5

1/5 = x^1

x = 1/5

x in { 1/4, 1/5 }