(9/2x)-(1/4)=(1/x)

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Solution for (9/2x)-(1/4)=(1/x) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(9/2)*x-(1/4) = 1/x // - 1/x

(9/2)*x-(1/x)-(1/4) = 0

(9/2)*x-x^-1-1/4 = 0

9/2*x^1-1*x^-1-1/4*x^0 = 0

(9/2*x^2-1/4*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(9/2*x^2-1/4*x^1-1*x^0) = 0

x^1

(9/2)*x^2+(-1/4)*x-1 = 0

(9/2)*x^2+(-1/4)*x-1 = 0

DELTA = (-1/4)^2-(-1*4*(9/2))

DELTA = 289/16

DELTA > 0

x = ((289/16)^(1/2)-(-1/4))/(2*(9/2)) or x = (-(-1/4)-(289/16)^(1/2))/(2*(9/2))

x = 1/2 or x = -4/9

x in { -4/9, 1/2} 

x in { -4/9, 1/2 }

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