(3/x-2)=(x-8/13)

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Solution for (3/x-2)=(x-8/13) equation: 


D( x )

x = 0

x = 0

x = 0

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

3/x-2 = x-(8/13) // - x-(8/13)

3/x-x+8/13-2 = 0

3*x^-1-1*x^1-18/13*x^0 = 0

(3*x^0-1*x^2-18/13*x^1)/(x^1) = 0 // * x^2

x^1*(3*x^0-1*x^2-18/13*x^1) = 0

x^1

(-18/13)*x-x^2+3 = 0

(-18/13)*x-x^2+3 = 0

DELTA = (-18/13)^2-(-1*3*4)

DELTA = 2352/169

DELTA > 0

x = ((2352/169)^(1/2)-(-18/13))/(-1*2) or x = (-(-18/13)-(2352/169)^(1/2))/(-1*2)

x = ((2352/169)^(1/2)+18/13)/(-2) or x = (18/13-(2352/169)^(1/2))/(-2)

x in { ((2352/169)^(1/2)+18/13)/(-2), (18/13-(2352/169)^(1/2))/(-2)} 

x in { ((2352/169)^(1/2)+18/13)/(-2), (18/13-(2352/169)^(1/2))/(-2) }

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