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

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


D( x )

x = 0

x = 0

x = 0

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

1/2-((1/3)*x) = 1/x-4 // - 1/x-4

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

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

9/2*x^0-1/3*x^1-1*x^-1 = 0

(9/2*x^1-1/3*x^2-1*x^0)/(x^1) = 0 // * x^2

x^1*(9/2*x^1-1/3*x^2-1*x^0) = 0

x^1

(-1/3)*x^2+(9/2)*x-1 = 0

(-1/3)*x^2+(9/2)*x-1 = 0

DELTA = (9/2)^2-(-1*4*(-1/3))

DELTA = 227/12

DELTA > 0

x = ((227/12)^(1/2)-(9/2))/(2*(-1/3)) or x = (-(9/2)-(227/12)^(1/2))/(2*(-1/3))

x = -3/2*((227/12)^(1/2)-9/2) or x = 3/2*((227/12)^(1/2)+9/2)

x in { -3/2*((227/12)^(1/2)-9/2), 3/2*((227/12)^(1/2)+9/2)} 

x in { -3/2*((227/12)^(1/2)-9/2), 3/2*((227/12)^(1/2)+9/2) }

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