ln((x^2-7)/(x))

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Solution for ln((x^2-7)/(x)) equation: 


D( x )

(x^2-7)/x <= 0

x = 0

(x^2-7)/x <= 0

(x^2-7)/x <= 0

( x )

x+0 <= 0 // - 0

x <= 0

( x^2-7 )

1*x^2 <= 7

1*x^2 <= 7 // : 1

x^2 <= 7/1

x^2 <= 7

x^2 <= 7 // ^ 1/2

abs(x) <= 7^(1/2)

x in <-7^(1/2):7^(1/2)>

	(-oo:-7^(1/2))	(-7^(1/2):0)	(0:7^(1/2))	(7^(1/2):+oo)
x	-	-	+	+
x^2-7	+	-	-	+


x = 0

x = 0

x in (-7^(1/2):0) U (7^(1/2):+oo)

ln((x^2-7)/x) = 0

ln((x^2-7)/x) = ln(e^0)

(x^2-7)/x = e^0

(x^2-7)/x-e^0 = 0

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

(x^2-7)/x+(-1*x)/x = 0

x^2-1*x-7 = 0

x^2-x-7 = 0

x^2-x-7 = 0

x^2-x-7 = 0

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

DELTA = 29

DELTA > 0

x = (29^(1/2)+1)/(1*2) or x = (1-29^(1/2))/(1*2)

x = (29^(1/2)+1)/2 or x = (1-29^(1/2))/2

(x-((1-29^(1/2))/2))*(x-((29^(1/2)+1)/2)) = 0

((x-((1-29^(1/2))/2))*(x-((29^(1/2)+1)/2)))/x = 0

((x-((1-29^(1/2))/2))*(x-((29^(1/2)+1)/2)))/x = 0 // * x

(x-((1-29^(1/2))/2))*(x-((29^(1/2)+1)/2)) = 0

( x-((1-29^(1/2))/2) )

x-((1-29^(1/2))/2) = 0 // + (1-29^(1/2))/2

x = (1-29^(1/2))/2

( x-((29^(1/2)+1)/2) )

x-((29^(1/2)+1)/2) = 0 // + (29^(1/2)+1)/2

x = (29^(1/2)+1)/2

x in { (1-29^(1/2))/2, (29^(1/2)+1)/2 }

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