(x/2x+18)-(81/x^2-81)=0

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Solution for (x/2x+18)-(81/x^2-81)=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-(81/(x^2))+18+81 = 0

(x/2)*x-81*x^-2+18+81 = 0

1/2*x^2-81*x^-2+99 = 0

t_1 = x^2

1/2*t_1^1-81*t_1^-1+99 = 0

1/2*t_1^1-81*t_1^-1+99*t_1^0 = 0

(1/2*t_1^2+99*t_1^1-81*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1/2*t_1^2+99*t_1^1-81*t_1^0) = 0

t_1^1

(1/2)*t_1^2+99*t_1-81 = 0

(1/2)*t_1^2+99*t_1-81 = 0

DELTA = 99^2-(-81*4*(1/2))

DELTA = 9963

DELTA > 0

t_1 = (9963^(1/2)-99)/(2*(1/2)) or t_1 = (-9963^(1/2)-99)/(2*(1/2))

t_1 = 9*123^(1/2)-99 or t_1 = -9*123^(1/2)-99

t_1 in { -9*123^(1/2)-99, 9*123^(1/2)-99}

t_1 = -9*123^(1/2)-99

x^2-(-9*123^(1/2))+99 = 0

x^2+9*123^(1/2)+99 = 0

1*x^2 = -(9*123^(1/2)+99) // : 1

x^2 = -(9*123^(1/2)+99)

t_1 = 9*123^(1/2)-99

x^2-(9*123^(1/2))+99 = 0

x^2-9*123^(1/2)+99 = 0

1*x^2 = -(99-9*123^(1/2)) // : 1

x^2 = -(99-9*123^(1/2))

x^2 = -(99-9*123^(1/2)) // ^ 1/2

abs(x) = (-(99-9*123^(1/2)))^(1/2)

x = (-(99-9*123^(1/2)))^(1/2) or x = -(-(99-9*123^(1/2)))^(1/2)

x in { (-(99-9*123^(1/2)))^(1/2), -(-(99-9*123^(1/2)))^(1/2) }

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