1-1/x=30/x^2

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

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

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

t_1 = x^-1

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

1-30*t_1^2-t_1 = 0

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

DELTA = 121

DELTA > 0

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

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

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

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

x in { -5, 6 }

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