6/x-1/4=3/4x

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Solution for 6/x-1/4=3/4x equation:


D( x )

x = 0

x = 0

x = 0

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

6/x-(1/4) = (3/4)*x // - (3/4)*x

6/x-((3/4)*x)-(1/4) = 0

(-3/4)*x+6/x-1/4 = 0

6*x^-1-3/4*x^1-1/4*x^0 = 0

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

x^1*(6*x^0-3/4*x^2-1/4*x^1) = 0

x^1

(-3/4)*x^2+(-1/4)*x+6 = 0

(-3/4)*x^2+(-1/4)*x+6 = 0

DELTA = (-1/4)^2-(4*6*(-3/4))

DELTA = 289/16

DELTA > 0

x = ((289/16)^(1/2)-(-1/4))/(2*(-3/4)) or x = (-(-1/4)-(289/16)^(1/2))/(2*(-3/4))

x = -3 or x = 8/3

x in { -3, 8/3}

x in { -3, 8/3 }

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