4/x-1-2/3x-3=-5/6

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Solution for 4/x-1-2/3x-3=-5/6 equation: 


D( x )

x = 0

x = 0

x = 0

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

4/x-((2/3)*x)-3-1 = -5/6 // + -5/6

4/x-((2/3)*x)-(-5/6)-3-1 = 0

(-2/3)*x+4/x+5/6-3-1 = 0

4*x^-1-2/3*x^1-19/6*x^0 = 0

(4*x^0-2/3*x^2-19/6*x^1)/(x^1) = 0 // * x^2

x^1*(4*x^0-2/3*x^2-19/6*x^1) = 0

x^1

(-2/3)*x^2+(-19/6)*x+4 = 0

(-2/3)*x^2+(-19/6)*x+4 = 0

DELTA = (-19/6)^2-(4*4*(-2/3))

DELTA = 745/36

DELTA > 0

x = ((745/36)^(1/2)-(-19/6))/(2*(-2/3)) or x = (-(-19/6)-(745/36)^(1/2))/(2*(-2/3))

x = -3/4*((745/36)^(1/2)+19/6) or x = -3/4*(19/6-(745/36)^(1/2))

x in { -3/4*((745/36)^(1/2)+19/6), -3/4*(19/6-(745/36)^(1/2))} 

x in { -3/4*((745/36)^(1/2)+19/6), -3/4*(19/6-(745/36)^(1/2)) }

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