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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

3*(x-2)^2-3*3*x*x+8*x = 0

8*x-6*x^2-12*x+12 = 0

12-6*x^2-4*x = 0

12-6*x^2-4*x = 0

2*(6-3*x^2-2*x) = 0

6-3*x^2-2*x = 0

DELTA = (-2)^2-(-3*4*6)

DELTA = 76

DELTA > 0

x = (76^(1/2)+2)/(-3*2) or x = (2-76^(1/2))/(-3*2)

x = (2*19^(1/2)+2)/(-6) or x = (2-2*19^(1/2))/(-6)

2*(x-((2*19^(1/2)+2)/(-6)))*(x-((2-2*19^(1/2))/(-6))) = 0

(2*(x-((2*19^(1/2)+2)/(-6)))*(x-((2-2*19^(1/2))/(-6))))/(3*x) = 0

(2*(x-((2*19^(1/2)+2)/(-6)))*(x-((2-2*19^(1/2))/(-6))))/(3*x) = 0 // * 3*x

2*(x-((2*19^(1/2)+2)/(-6)))*(x-((2-2*19^(1/2))/(-6))) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((2*19^(1/2)+2)/(-6)) )

x-((2*19^(1/2)+2)/(-6)) = 0 // + (2*19^(1/2)+2)/(-6)

x = (2*19^(1/2)+2)/(-6)

( x-((2-2*19^(1/2))/(-6)) )

x-((2-2*19^(1/2))/(-6)) = 0 // + (2-2*19^(1/2))/(-6)

x = (2-2*19^(1/2))/(-6)

x in { (2*19^(1/2)+2)/(-6), (2-2*19^(1/2))/(-6) }

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