(X-1/3)^2=1/4

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Solution for (X-1/3)^2=1/4 equation: 


X in (-oo:+oo)

(X-(1/3))^2 = 1/4 // - 1/4

(X-(1/3))^2-(1/4) = 0

(X-1/3)^2-1/4 = 0

(4*(X-1/3)^2)/4-1/4 = 0

4*(X-1/3)^2-1 = 0

4*X^2-8/3*X-5/9 = 0

4*X^2-8/3*X-5/9 = 0

4*X^2-8/3*X-5/9 = 0

DELTA = (-8/3)^2-(-5/9*4*4)

DELTA = 16

DELTA > 0

X = (16^(1/2)+8/3)/(2*4) or X = (8/3-16^(1/2))/(2*4)

X = 5/6 or X = -1/6

(X+1/6)*(X-5/6) = 0

((X+1/6)*(X-5/6))/4 = 0

((X+1/6)*(X-5/6))/4 = 0 // * 4

(X+1/6)*(X-5/6) = 0

( X+1/6 )

X+1/6 = 0 // - 1/6

X = -1/6

( X-5/6 )

X-5/6 = 0 // + 5/6

X = 5/6

X in { -1/6, 5/6 }

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