1-9/x-36/x^2=0

Solution for 1-9/x-36/x^2=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-(9/x)-(36/(x^2)) = 0

1-9*x^-1-36*x^-2 = 0

t_1 = x^-1

1-36*t_1^2-9*t_1^1 = 0

1-36*t_1^2-9*t_1 = 0

DELTA = (-9)^2-(-36*1*4)

DELTA = 225

DELTA > 0

t_1 = (225^(1/2)+9)/(-36*2) or t_1 = (9-225^(1/2))/(-36*2)

t_1 = -1/3 or t_1 = 1/12

t_1 = -1/3

x^-1+1/3 = 0

1*x^-1 = -1/3 // : 1

x^-1 = -1/3

-1 < 0

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

1 = -1/3*x^1 // : -1/3

-3 = x^1

x = -3

t_1 = 1/12

x^-1-1/12 = 0

1*x^-1 = 1/12 // : 1

x^-1 = 1/12

-1 < 0

1/(x^1) = 1/12 // * x^1

1 = 1/12*x^1 // : 1/12

12 = x^1

x = 12

x in { -3, 12 }