3x-2/(x-4)=8

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Solution for 3x-2/(x-4)=8 equation: 


D( x )

x-4 = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:+oo)

3*x-(2/(x-4)) = 8 // - 8

3*x-(2/(x-4))-8 = 0

3*x-2*(x-4)^-1-8 = 0

3*x-2/(x-4)-8 = 0

(3*x*(x-4))/(x-4)-2/(x-4)+(-8*(x-4))/(x-4) = 0

3*x*(x-4)-8*(x-4)-2 = 0

3*x^2-12*x-8*x-2+32 = 0

3*x^2-20*x+30 = 0

3*x^2-20*x+30 = 0

3*x^2-20*x+30 = 0

DELTA = (-20)^2-(3*4*30)

DELTA = 40

DELTA > 0

x = (40^(1/2)+20)/(2*3) or x = (20-40^(1/2))/(2*3)

x = (2*10^(1/2)+20)/6 or x = (20-2*10^(1/2))/6

(x-((20-2*10^(1/2))/6))*(x-((2*10^(1/2)+20)/6)) = 0

((x-((20-2*10^(1/2))/6))*(x-((2*10^(1/2)+20)/6)))/(x-4) = 0

((x-((20-2*10^(1/2))/6))*(x-((2*10^(1/2)+20)/6)))/(x-4) = 0 // * x-4

(x-((20-2*10^(1/2))/6))*(x-((2*10^(1/2)+20)/6)) = 0

( x-((2*10^(1/2)+20)/6) )

x-((2*10^(1/2)+20)/6) = 0 // + (2*10^(1/2)+20)/6

x = (2*10^(1/2)+20)/6

( x-((20-2*10^(1/2))/6) )

x-((20-2*10^(1/2))/6) = 0 // + (20-2*10^(1/2))/6

x = (20-2*10^(1/2))/6

x in { (2*10^(1/2)+20)/6, (20-2*10^(1/2))/6 }

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