2(x-4)^2/3=32

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Solution for 2(x-4)^2/3=32 equation: 


x in (-oo:+oo)

(2*(x-4)^2)/3 = 32 // - 32

(2*(x-4)^2)/3-32 = 0

(2*(x-4)^2)/3+(-32*3)/3 = 0

2*(x-4)^2-32*3 = 0

2*x^2-16*x-64 = 0

2*x^2-16*x-64 = 0

2*(x^2-8*x-32) = 0

x^2-8*x-32 = 0

DELTA = (-8)^2-(-32*1*4)

DELTA = 192

DELTA > 0

x = (192^(1/2)+8)/(1*2) or x = (8-192^(1/2))/(1*2)

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

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

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

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

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

( 2 )

2 = 0

x belongs to the empty set

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

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

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

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

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

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

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

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