9-1/x=8/x^2

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Solution for 9-1/x=8/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)

9-(1/x) = 8/(x^2) // - 8/(x^2)

9-(1/x)-(8/(x^2)) = 0

9-x^-1-8*x^-2 = 0

t_1 = x^-1

9-8*t_1^2-1*t_1^1 = 0

9-8*t_1^2-t_1 = 0

DELTA = (-1)^2-(-8*4*9)

DELTA = 289

DELTA > 0

t_1 = (289^(1/2)+1)/(-8*2) or t_1 = (1-289^(1/2))/(-8*2)

t_1 = -9/8 or t_1 = 1

t_1 = -9/8

x^-1+9/8 = 0

1*x^-1 = -9/8 // : 1

x^-1 = -9/8

-1 < 0

1/(x^1) = -9/8 // * x^1

1 = -9/8*x^1 // : -9/8

-8/9 = x^1

x = -8/9

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 { -8/9, 1 }

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