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

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Solution for 3/x-1/4=9/2x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

(-9/2)*x+3/x-1/4 = 0

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

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

x^1*(3*x^0-9/2*x^2-1/4*x^1) = 0

x^1

(-9/2)*x^2+(-1/4)*x+3 = 0

(-9/2)*x^2+(-1/4)*x+3 = 0

DELTA = (-1/4)^2-(3*4*(-9/2))

DELTA = 865/16

DELTA > 0

x = ((865/16)^(1/2)-(-1/4))/(2*(-9/2)) or x = (-(-1/4)-(865/16)^(1/2))/(2*(-9/2))

x = ((865/16)^(1/2)+1/4)/(-9) or x = (1/4-(865/16)^(1/2))/(-9)

x in { ((865/16)^(1/2)+1/4)/(-9), (1/4-(865/16)^(1/2))/(-9)} 

x in { ((865/16)^(1/2)+1/4)/(-9), (1/4-(865/16)^(1/2))/(-9) }

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