1+1/x=30/x^2

Solution for 1+1/x=30/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 = 30/(x^2) // - 30/(x^2)

1/x-(30/(x^2))+1 = 0

1/x-30*x^-2+1 = 0

x^-1-30*x^-2+1 = 0

t_1 = x^-1

1*t_1^1-30*t_1^2+1 = 0

t_1-30*t_1^2+1 = 0

DELTA = 1^2-(-30*1*4)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)-1)/(-30*2) or t_1 = (-121^(1/2)-1)/(-30*2)

t_1 = -1/6 or t_1 = 1/5

t_1 = -1/6

x^-1+1/6 = 0

1*x^-1 = -1/6 // : 1

x^-1 = -1/6

-1 < 0

1/(x^1) = -1/6 // * x^1

1 = -1/6*x^1 // : -1/6

-6 = x^1

x = -6

t_1 = 1/5

x^-1-1/5 = 0

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

x^-1 = 1/5

-1 < 0

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

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

5 = x^1

x = 5

x in { -6, 5 }