(2/3x)+(4/x)=(7/x+1)

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Solution for (2/3x)+(4/x)=(7/x+1) equation: 


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x+4/x = 7/x+1 // - 7/x+1

(2/3)*x+4/x-(7/x)-1 = 0

(2/3)*x+4/x-7*x^-1-1 = 0

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

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

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

x^1

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

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

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

DELTA = 9

DELTA > 0

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

x = 3 or x = -3/2

x in { -3/2, 3} 

x in { -3/2, 3 }

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