1+1/x=72/x^2

Solution for 1+1/x=72/x^2 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+1 = 72/(x^2) // - 72/(x^2)

1/x-(72/(x^2))+1 = 0

1/x-72*x^-2+1 = 0

x^-1-72*x^-2+1 = 0

t_1 = x^-1

1*t_1^1-72*t_1^2+1 = 0

t_1-72*t_1^2+1 = 0

DELTA = 1^2-(-72*1*4)

DELTA = 289

DELTA > 0

t_1 = (289^(1/2)-1)/(-72*2) or t_1 = (-289^(1/2)-1)/(-72*2)

t_1 = -1/9 or t_1 = 1/8

t_1 = -1/9

x^-1+1/9 = 0

1*x^-1 = -1/9 // : 1

x^-1 = -1/9

-1 < 0

1/(x^1) = -1/9 // * x^1

1 = -1/9*x^1 // : -1/9

-9 = x^1

x = -9

t_1 = 1/8

x^-1-1/8 = 0

1*x^-1 = 1/8 // : 1

x^-1 = 1/8

-1 < 0

1/(x^1) = 1/8 // * x^1

1 = 1/8*x^1 // : 1/8

8 = x^1

x = 8

x in { -9, 8 }