8X-5/X-1=10/6

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Solution for 8X-5/X-1=10/6 equation: 


D( X )

X = 0

X = 0

X = 0

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

8*X-(5/X)-1 = 10/6 // - 10/6

8*X-(5/X)-(10/6)-1 = 0

8*X-5*X^-1-5/3-1 = 0

8*X^1-5*X^-1-8/3*X^0 = 0

(8*X^2-8/3*X^1-5*X^0)/(X^1) = 0 // * X^2

X^1*(8*X^2-8/3*X^1-5*X^0) = 0

X^1

8*X^2+(-8/3)*X-5 = 0

8*X^2+(-8/3)*X-5 = 0

DELTA = (-8/3)^2-(-5*4*8)

DELTA = 1504/9

DELTA > 0

X = ((1504/9)^(1/2)-(-8/3))/(2*8) or X = (-(-8/3)-(1504/9)^(1/2))/(2*8)

X = ((1504/9)^(1/2)+8/3)/16 or X = (8/3-(1504/9)^(1/2))/16

X in { (8/3-(1504/9)^(1/2))/16, ((1504/9)^(1/2)+8/3)/16} 

X in { (8/3-(1504/9)^(1/2))/16, ((1504/9)^(1/2)+8/3)/16 }

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