1/3(x-4)^2/3=12

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Solution for 1/3(x-4)^2/3=12 equation: 


x in (-oo:+oo)

((1/3)*(x-4)^2)/3 = 12 // - 12

((1/3)*(x-4)^2)/3-12 = 0

(1/3*(x-4)^2)/3-12 = 0

(1/3*(x-4)^2)/3+(-12*3)/3 = 0

1/3*(x-4)^2-12*3 = 0

1/3*x^2-8/3*x-92/3 = 0

1/3*x^2-8/3*x-92/3 = 0

1/3*(x^2-8*x-92) = 0

x^2-8*x-92 = 0

DELTA = (-8)^2-(-92*1*4)

DELTA = 432

DELTA > 0

x = (432^(1/2)+8)/(1*2) or x = (8-432^(1/2))/(1*2)

x = (12*3^(1/2)+8)/2 or x = (8-12*3^(1/2))/2

1/3*(x-((8-12*3^(1/2))/2))*(x-((12*3^(1/2)+8)/2)) = 0

(1/3*(x-((8-12*3^(1/2))/2))*(x-((12*3^(1/2)+8)/2)))/3 = 0

(1/3*(x-((8-12*3^(1/2))/2))*(x-((12*3^(1/2)+8)/2)))/3 = 0 // * 3

1/3*(x-((8-12*3^(1/2))/2))*(x-((12*3^(1/2)+8)/2)) = 0

( 1/3 )

1/3 = 0

x belongs to the empty set

( x-((12*3^(1/2)+8)/2) )

x-((12*3^(1/2)+8)/2) = 0 // + (12*3^(1/2)+8)/2

x = (12*3^(1/2)+8)/2

( x-((8-12*3^(1/2))/2) )

x-((8-12*3^(1/2))/2) = 0 // + (8-12*3^(1/2))/2

x = (8-12*3^(1/2))/2

x in { (12*3^(1/2)+8)/2, (8-12*3^(1/2))/2 }

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