x/2x+6-5/x^2-9=0

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Solution for x/2x+6-5/x^2-9=0 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/2)*x-(5/(x^2))-9+6 = 0

(x/2)*x-5*x^-2-9+6 = 0

1/2*x^2-5*x^-2-3 = 0

t_1 = x^2

1/2*t_1^1-5*t_1^-1-3 = 0

1/2*t_1^1-5*t_1^-1-3*t_1^0 = 0

(1/2*t_1^2-3*t_1^1-5*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1/2*t_1^2-3*t_1^1-5*t_1^0) = 0

t_1^1

(1/2)*t_1^2-3*t_1-5 = 0

(1/2)*t_1^2-3*t_1-5 = 0

DELTA = (-3)^2-(-5*4*(1/2))

DELTA = 19

DELTA > 0

t_1 = (19^(1/2)+3)/(2*(1/2)) or t_1 = (3-19^(1/2))/(2*(1/2))

t_1 = 19^(1/2)+3 or t_1 = 3-19^(1/2)

t_1 in { 3-19^(1/2), 19^(1/2)+3} 

t_1 = 3-19^(1/2)

x^2+19^(1/2)-3 = 0

1*x^2 = -(19^(1/2)-3) // : 1

x^2 = 3-19^(1/2)

t_1 = 19^(1/2)+3

x^2-19^(1/2)-3 = 0

1*x^2 = 19^(1/2)+3 // : 1

x^2 = 19^(1/2)+3

x^2 = 19^(1/2)+3 // ^ 1/2

abs(x) = (19^(1/2)+3)^(1/2)

x = (19^(1/2)+3)^(1/2) or x = -(19^(1/2)+3)^(1/2)

x in { (19^(1/2)+3)^(1/2), -(19^(1/2)+3)^(1/2) }

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