6/2x-5=4/x-9

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Solution for 6/2x-5=4/x-9 equation: 


D( x )

x = 0

x = 0

x = 0

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

(6/2)*x-5 = 4/x-9 // - 4/x-9

(6/2)*x-(4/x)-5+9 = 0

(6/2)*x-4*x^-1-5+9 = 0

3*x^1-4*x^-1+4*x^0 = 0

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

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

x^1

3*x^2+4*x-4 = 0

3*x^2+4*x-4 = 0

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

DELTA = 64

DELTA > 0

x = (64^(1/2)-4)/(2*3) or x = (-64^(1/2)-4)/(2*3)

x = 2/3 or x = -2

x in { -2, 2/3} 

x in { -2, 2/3 }

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