(1/2)-(3/(2x+3))=(3/(x-4))

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Solution for (1/2)-(3/(2x+3))=(3/(x-4)) equation: 


D( x )

x-4 = 0

2*x+3 = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

x in (-oo:-3/2) U (-3/2:4) U (4:+oo)

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

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

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

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

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

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

2*x^2-18*x-5*x-12+6 = 0

2*x^2-23*x-6 = 0

2*x^2-23*x-6 = 0

2*x^2-23*x-6 = 0

DELTA = (-23)^2-(-6*2*4)

DELTA = 577

DELTA > 0

x = (577^(1/2)+23)/(2*2) or x = (23-577^(1/2))/(2*2)

x = (577^(1/2)+23)/4 or x = (23-577^(1/2))/4

(x-((23-577^(1/2))/4))*(x-((577^(1/2)+23)/4)) = 0

((x-((23-577^(1/2))/4))*(x-((577^(1/2)+23)/4)))/(2*(2*x+3)*(x-4)) = 0

((x-((23-577^(1/2))/4))*(x-((577^(1/2)+23)/4)))/(2*(2*x+3)*(x-4)) = 0 // * 2*(2*x+3)*(x-4)

(x-((23-577^(1/2))/4))*(x-((577^(1/2)+23)/4)) = 0

( x-((23-577^(1/2))/4) )

x-((23-577^(1/2))/4) = 0 // + (23-577^(1/2))/4

x = (23-577^(1/2))/4

( x-((577^(1/2)+23)/4) )

x-((577^(1/2)+23)/4) = 0 // + (577^(1/2)+23)/4

x = (577^(1/2)+23)/4

x in { (23-577^(1/2))/4, (577^(1/2)+23)/4 }

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