(2/3x)=((x+3)/(2x-5))

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Solution for (2/3x)=((x+3)/(2x-5)) equation: 


D( x )

2*x-5 = 0

2*x-5 = 0

2*x-5 = 0

2*x-5 = 0 // + 5

2*x = 5 // : 2

x = 5/2

x in (-oo:5/2) U (5/2:+oo)

(2/3)*x = (x+3)/(2*x-5) // - (x+3)/(2*x-5)

(2/3)*x-((x+3)/(2*x-5)) = 0

(-1*(x+3))/(2*x-5)+(2*x)/3 = 0

(-1*3*(x+3))/(3*(2*x-5))+(2*x*(2*x-5))/(3*(2*x-5)) = 0

2*x*(2*x-5)-1*3*(x+3) = 0

4*x^2-13*x-9 = 0

4*x^2-13*x-9 = 0

4*x^2-13*x-9 = 0

DELTA = (-13)^2-(-9*4*4)

DELTA = 313

DELTA > 0

x = (313^(1/2)+13)/(2*4) or x = (13-313^(1/2))/(2*4)

x = (313^(1/2)+13)/8 or x = (13-313^(1/2))/8

(x-((13-313^(1/2))/8))*(x-((313^(1/2)+13)/8)) = 0

((x-((13-313^(1/2))/8))*(x-((313^(1/2)+13)/8)))/(3*(2*x-5)) = 0

((x-((13-313^(1/2))/8))*(x-((313^(1/2)+13)/8)))/(3*(2*x-5)) = 0 // * 3*(2*x-5)

(x-((13-313^(1/2))/8))*(x-((313^(1/2)+13)/8)) = 0

( x-((13-313^(1/2))/8) )

x-((13-313^(1/2))/8) = 0 // + (13-313^(1/2))/8

x = (13-313^(1/2))/8

( x-((313^(1/2)+13)/8) )

x-((313^(1/2)+13)/8) = 0 // + (313^(1/2)+13)/8

x = (313^(1/2)+13)/8

x in { (13-313^(1/2))/8, (313^(1/2)+13)/8 }

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