6/7x+3=4/x-2

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Solution for 6/7x+3=4/x-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

(6/7)*x+3 = 4/x-2 // - 4/x-2

(6/7)*x-(4/x)+2+3 = 0

(6/7)*x-4*x^-1+2+3 = 0

6/7*x^1-4*x^-1+5*x^0 = 0

(6/7*x^2+5*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(6/7*x^2+5*x^1-4*x^0) = 0

x^1

(6/7)*x^2+5*x-4 = 0

(6/7)*x^2+5*x-4 = 0

DELTA = 5^2-(-4*4*(6/7))

DELTA = 271/7

DELTA > 0

x = ((271/7)^(1/2)-5)/(2*(6/7)) or x = (-(271/7)^(1/2)-5)/(2*(6/7))

x = 7/12*((271/7)^(1/2)-5) or x = -7/12*((271/7)^(1/2)+5)

x in { -7/12*((271/7)^(1/2)+5), 7/12*((271/7)^(1/2)-5)} 

x in { -7/12*((271/7)^(1/2)+5), 7/12*((271/7)^(1/2)-5) }

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