(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))+6+9 = 0

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

1/2*x^2-5*x^-2+15 = 0

t_1 = x^2

1/2*t_1^1-5*t_1^-1+15 = 0

1/2*t_1^1-5*t_1^-1+15*t_1^0 = 0

(1/2*t_1^2+15*t_1^1-5*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1/2*t_1^2+15*t_1^1-5*t_1^0) = 0

t_1^1

(1/2)*t_1^2+15*t_1-5 = 0

(1/2)*t_1^2+15*t_1-5 = 0

DELTA = 15^2-(-5*4*(1/2))

DELTA = 235

DELTA > 0

t_1 = (235^(1/2)-15)/(2*(1/2)) or t_1 = (-235^(1/2)-15)/(2*(1/2))

t_1 = 235^(1/2)-15 or t_1 = -(235^(1/2)+15)

t_1 in { -(235^(1/2)+15), 235^(1/2)-15} 

t_1 = -(235^(1/2)+15)

x^2+235^(1/2)+15 = 0

1*x^2 = -(235^(1/2)+15) // : 1

x^2 = -(235^(1/2)+15)

t_1 = 235^(1/2)-15

x^2-235^(1/2)+15 = 0

1*x^2 = -(15-235^(1/2)) // : 1

x^2 = 235^(1/2)-15

x^2 = 235^(1/2)-15 // ^ 1/2

abs(x) = (235^(1/2)-15)^(1/2)

x = (235^(1/2)-15)^(1/2) or x = -(235^(1/2)-15)^(1/2)

x in { (235^(1/2)-15)^(1/2), -(235^(1/2)-15)^(1/2) }

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