x-3/2=5/x

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Solution for x-3/2=5/x equation:


D( x )

x = 0

x = 0

x = 0

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

x-(3/2) = 5/x // - 5/x

x-(5/x)-(3/2) = 0

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

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

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

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

x^1

x^2+(-3/2)*x-5 = 0

x^2+(-3/2)*x-5 = 0

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

DELTA = 89/4

DELTA > 0

x = ((89/4)^(1/2)-(-3/2))/(1*2) or x = (-(-3/2)-(89/4)^(1/2))/(1*2)

x = ((89/4)^(1/2)+3/2)/2 or x = (3/2-(89/4)^(1/2))/2

x in { (3/2-(89/4)^(1/2))/2, ((89/4)^(1/2)+3/2)/2}

x in { (3/2-(89/4)^(1/2))/2, ((89/4)^(1/2)+3/2)/2 }

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