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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 35/12

DELTA > 0

x = ((35/12)^(1/2)-(-1/2))/(2*(1/3)) or x = (-(-1/2)-(35/12)^(1/2))/(2*(1/3))

x = 3/2*((35/12)^(1/2)+1/2) or x = 3/2*(1/2-(35/12)^(1/2))

x in { 3/2*(1/2-(35/12)^(1/2)), 3/2*((35/12)^(1/2)+1/2)} 

x in { 3/2*(1/2-(35/12)^(1/2)), 3/2*((35/12)^(1/2)+1/2) }

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