12/4x-1=3/x

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Solution for 12/4x-1=3/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(12/4)*x-1 = 3/x // - 3/x

(12/4)*x-(3/x)-1 = 0

(12/4)*x-3*x^-1-1 = 0

3*x^1-3*x^-1-1*x^0 = 0

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

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

x^1

3*x^2-x-3 = 0

3*x^2-x-3 = 0

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

DELTA = 37

DELTA > 0

x = (37^(1/2)+1)/(2*3) or x = (1-37^(1/2))/(2*3)

x = (37^(1/2)+1)/6 or x = (1-37^(1/2))/6

x in { (1-37^(1/2))/6, (37^(1/2)+1)/6} 

x in { (1-37^(1/2))/6, (37^(1/2)+1)/6 }

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