1/3(x-10)^2-8=16

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Solution for 1/3(x-10)^2-8=16 equation: 


x in (-oo:+oo)

(1/3)*(x-10)^2-8 = 16 // - 16

(1/3)*(x-10)^2-16-8 = 0

1/3*(x-10)^2-16-8 = 0

1/3*(x-10)^2-16-8 = 0

1/3*x^2-20/3*x-8+52/3 = 0

1/3*x^2-20/3*x+28/3 = 0

1/3*x^2-20/3*x+28/3 = 0

1/3*(x^2-20*x+28) = 0

x^2-20*x+28 = 0

DELTA = (-20)^2-(1*4*28)

DELTA = 288

DELTA > 0

x = (288^(1/2)+20)/(1*2) or x = (20-288^(1/2))/(1*2)

x = (12*2^(1/2)+20)/2 or x = (20-12*2^(1/2))/2

1/3*(x-((20-12*2^(1/2))/2))*(x-((12*2^(1/2)+20)/2)) = 0

1/3*(x-((20-12*2^(1/2))/2))*(x-((12*2^(1/2)+20)/2)) = 0

( 1/3 )

1/3 = 0

x belongs to the empty set

( x-((12*2^(1/2)+20)/2) )

x-((12*2^(1/2)+20)/2) = 0 // + (12*2^(1/2)+20)/2

x = (12*2^(1/2)+20)/2

( x-((20-12*2^(1/2))/2) )

x-((20-12*2^(1/2))/2) = 0 // + (20-12*2^(1/2))/2

x = (20-12*2^(1/2))/2

x in { (12*2^(1/2)+20)/2, (20-12*2^(1/2))/2 }

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