5/x^2-x-6

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Solution for 5/x^2-x-6 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)

5/(x^2)-x-6 = 0

5*x^-2-1*x^1-6*x^0 = 0

(5*x^0-1*x^3-6*x^2)/(x^2) = 0 // * x^4

x^2*(5*x^0-1*x^3-6*x^2) = 0

x^2

5-x^3-6*x^2 = 0

{ 1, -1, 5, -5 }

1

x = 1

5-x^3-6*x^2 = -2

1

-1

x = -1

5-x^3-6*x^2 = 0

-1

x+1

5-x^2-5*x

5-x^3-6*x^2

x+1

x^3+x^2

5-5*x^2

5*x^2+5*x

5*x+5

-5*x-5

0

5-x^2-5*x = 0

DELTA = (-5)^2-(-1*4*5)

DELTA = 45

DELTA > 0

x = (45^(1/2)+5)/(-1*2) or x = (5-45^(1/2))/(-1*2)

x = (3*5^(1/2)+5)/(-2) or x = (5-3*5^(1/2))/(-2)

x in { (3*5^(1/2)+5)/(-2), (5-3*5^(1/2))/(-2), -1} 

x in { (3*5^(1/2)+5)/(-2), (5-3*5^(1/2))/(-2), -1 }

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