(X-1/2)^2=9/4

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Solution for (X-1/2)^2=9/4 equation: 


X in (-oo:+oo)

(X-(1/2))^2 = 9/4 // - 9/4

(X-(1/2))^2-(9/4) = 0

(X-1/2)^2-9/4 = 0

(4*(X-1/2)^2)/4-9/4 = 0

4*(X-1/2)^2-9 = 0

4*X^2-4*X-8 = 0

4*X^2-4*X-8 = 0

4*(X^2-X-2) = 0

X^2-X-2 = 0

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

DELTA = 9

DELTA > 0

X = (9^(1/2)+1)/(1*2) or X = (1-9^(1/2))/(1*2)

X = 2 or X = -1

4*(X+1)*(X-2) = 0

(4*(X+1)*(X-2))/4 = 0

(4*(X+1)*(X-2))/4 = 0 // * 4

4*(X+1)*(X-2) = 0

( X+1 )

X+1 = 0 // - 1

X = -1

( X-2 )

X-2 = 0 // + 2

X = 2

X in { -1, 2 }

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