0=(x-2)^3/2-3(x-2)^1/2

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Solution for 0=(x-2)^3/2-3(x-2)^1/2 equation: 


x in (-oo:+oo)

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

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

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

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

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

6*x^2-x^3-9*x+2 = 0

6*x^2-x^3-9*x+2 = 0

6*x^2-x^3-9*x+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

6*x^2-x^3-9*x+2 = -2

1

-1

x = -1

6*x^2-x^3-9*x+2 = 18

-1

2

x = 2

6*x^2-x^3-9*x+2 = 0

2

x-2

4*x-x^2-1

6*x^2-x^3-9*x+2

x-2

x^3-2*x^2

4*x^2-9*x+2

8*x-4*x^2

2-x

x-2

0

4*x-x^2-1 = 0

DELTA = 4^2-(-1*(-1)*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)-4)/(-1*2) or x = (-12^(1/2)-4)/(-1*2)

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

x in { (2*3^(1/2)-4)/(-2), (-2*3^(1/2)-4)/(-2), 2} 

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

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

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

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

( x-((-2*3^(1/2)-4)/(-2)) )

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

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

( x-((2*3^(1/2)-4)/(-2)) )

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

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

( x-2 )

x-2 = 0 // + 2

x = 2

x in { (-2*3^(1/2)-4)/(-2), (2*3^(1/2)-4)/(-2), 2 }

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