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x in (-oo:+oo)
(2*x-(1/2))^2 = 9/4 // - 9/4
(2*x-(1/2))^2-(9/4) = 0
(2*x-1/2)^2-9/4 = 0
(4*(2*x-1/2)^2)/4-9/4 = 0
4*(2*x-1/2)^2-9 = 0
16*x^2-8*x-8 = 0
16*x^2-8*x-8 = 0
8*(2*x^2-x-1) = 0
2*x^2-x-1 = 0
DELTA = (-1)^2-(-1*2*4)
DELTA = 9
DELTA > 0
x = (9^(1/2)+1)/(2*2) or x = (1-9^(1/2))/(2*2)
x = 1 or x = -1/2
8*(x+1/2)*(x-1) = 0
(8*(x+1/2)*(x-1))/4 = 0
(8*(x+1/2)*(x-1))/4 = 0 // * 4
8*(x+1/2)*(x-1) = 0
( 8 )
8 = 0
x belongs to the empty set
( x+1/2 )
x+1/2 = 0 // - 1/2
x = -1/2
( x-1 )
x-1 = 0 // + 1
x = 1
x in { -1/2, 1 }
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