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

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


x in (-oo:+oo)

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

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

x^2-x-1 = 0

x^2-x-1 = 0

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

DELTA = 5

DELTA > 0

x = (5^(1/2)+1)/(1*2) or x = (1-5^(1/2))/(1*2)

x = (5^(1/2)+1)/2 or x = (1-5^(1/2))/2

(x-((1-5^(1/2))/2))*(x-((5^(1/2)+1)/2)) = 0

1/2*(x-((1-5^(1/2))/2))*(x-((5^(1/2)+1)/2)) = 0

( 1/2 )

1/2 = 0

x belongs to the empty set

( x-((1-5^(1/2))/2) )

x-((1-5^(1/2))/2) = 0 // + (1-5^(1/2))/2

x = (1-5^(1/2))/2

( x-((5^(1/2)+1)/2) )

x-((5^(1/2)+1)/2) = 0 // + (5^(1/2)+1)/2

x = (5^(1/2)+1)/2

x in { (1-5^(1/2))/2, (5^(1/2)+1)/2 }

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