3/x=3x-3/2

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


D( x )

x = 0

x = 0

x = 0

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

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

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

3/x-3*x+3/2 = 0

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

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

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

x^1

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

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

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

DELTA = 153/4

DELTA > 0

x = ((153/4)^(1/2)-(3/2))/(-3*2) or x = (-(3/2)-(153/4)^(1/2))/(-3*2)

x = ((153/4)^(1/2)-3/2)/(-6) or x = ((153/4)^(1/2)+3/2)/6

x in { ((153/4)^(1/2)-3/2)/(-6), ((153/4)^(1/2)+3/2)/6}

x in { ((153/4)^(1/2)-3/2)/(-6), ((153/4)^(1/2)+3/2)/6 }

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