(3z-1)^2=4/9

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Solution for (3z-1)^2=4/9 equation: 


z in (-oo:+oo)

(3*z-1)^2 = 4/9 // - 4/9

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

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

(9*(3*z-1)^2)/9-4/9 = 0

9*(3*z-1)^2-4 = 0

81*z^2-54*z+5 = 0

81*z^2-54*z+5 = 0

81*z^2-54*z+5 = 0

DELTA = (-54)^2-(4*5*81)

DELTA = 1296

DELTA > 0

z = (1296^(1/2)+54)/(2*81) or z = (54-1296^(1/2))/(2*81)

z = 5/9 or z = 1/9

(z-1/9)*(z-5/9) = 0

((z-1/9)*(z-5/9))/9 = 0

((z-1/9)*(z-5/9))/9 = 0 // * 9

(z-1/9)*(z-5/9) = 0

( z-1/9 )

z-1/9 = 0 // + 1/9

z = 1/9

( z-5/9 )

z-5/9 = 0 // + 5/9

z = 5/9

z in { 1/9, 5/9 }

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