(x-9)^2/x^2-81

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Solution for (x-9)^2/x^2-81 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

((x-9)^2)/(x^2)-81 = 0

((x-9)^2)/(x^2)+(-81*x^2)/(x^2) = 0

(x-9)^2-81*x^2 = 0

81-80*x^2-18*x = 0

81-80*x^2-18*x = 0

81-80*x^2-18*x = 0

DELTA = (-18)^2-(-80*4*81)

DELTA = 26244

DELTA > 0

x = (26244^(1/2)+18)/(-80*2) or x = (18-26244^(1/2))/(-80*2)

x = -9/8 or x = 9/10

(x+9/8)*(x-9/10) = 0

((x+9/8)*(x-9/10))/(x^2) = 0

((x+9/8)*(x-9/10))/(x^2) = 0 // * x^2

(x+9/8)*(x-9/10) = 0

( x+9/8 )

x+9/8 = 0 // - 9/8

x = -9/8

( x-9/10 )

x-9/10 = 0 // + 9/10

x = 9/10

x in { -9/8, 9/10 }

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