3/4+1/3x=2/x-5/12

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Solution for 3/4+1/3x=2/x-5/12 equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/3)*x+3/4 = 2/x-(5/12) // - 2/x-(5/12)

(1/3)*x-(2/x)+3/4+5/12 = 0

(1/3)*x-2*x^-1+3/4+5/12 = 0

1/3*x^1-2*x^-1+7/6*x^0 = 0

(1/3*x^2+7/6*x^1-2*x^0)/(x^1) = 0 // * x^2

x^1*(1/3*x^2+7/6*x^1-2*x^0) = 0

x^1

(1/3)*x^2+(7/6)*x-2 = 0

(1/3)*x^2+(7/6)*x-2 = 0

DELTA = (7/6)^2-(-2*4*(1/3))

DELTA = 145/36

DELTA > 0

x = ((145/36)^(1/2)-(7/6))/(2*(1/3)) or x = (-(7/6)-(145/36)^(1/2))/(2*(1/3))

x = 3/2*((145/36)^(1/2)-7/6) or x = -3/2*((145/36)^(1/2)+7/6)

x in { -3/2*((145/36)^(1/2)+7/6), 3/2*((145/36)^(1/2)-7/6)} 

x in { -3/2*((145/36)^(1/2)+7/6), 3/2*((145/36)^(1/2)-7/6) }

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