5/x^2+x-6

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)

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

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

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

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

x^2

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

{ 1, -1, 5, -5 }

1

x = 1

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

1

x-1

x^2-5*x-5

x^3-6*x^2+5

x-1

x^2-x^3

5-5*x^2

5*x^2-5*x

5-5*x

5*x-5

0

x^2-5*x-5 = 0

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

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

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