1-(7/x)=-6/x^2

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Solution for 1-(7/x)=-6/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-(7/x) = -6/(x^2) // + -6/(x^2)

1-(7/x)-(-6/(x^2)) = 0

6*x^-2-7*x^-1+1 = 0

t_1 = x^-1

6*t_1^2-7*t_1^1+1 = 0

6*t_1^2-7*t_1+1 = 0

DELTA = (-7)^2-(1*4*6)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+7)/(2*6) or t_1 = (7-25^(1/2))/(2*6)

t_1 = 1 or t_1 = 1/6

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

x^-1-1 = 0

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

x^-1 = 1

-1 < 0

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

1 = 1*x^1 // : 1

1 = x^1

x = 1

x in { 6, 1 }

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