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

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

X in (-oo:+oo)

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

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

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

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

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

4*X^2-36*X+72 = 0

4*X^2-36*X+72 = 0

4*(X^2-9*X+18) = 0

X^2-9*X+18 = 0

DELTA = (-9)^2-(1*4*18)

DELTA = 9

DELTA > 0

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

X = 6 or X = 3

4*(X-3)*(X-6) = 0

(4*(X-3)*(X-6))/4 = 0

(4*(X-3)*(X-6))/4 = 0 // * 4

4*(X-3)*(X-6) = 0

( 4 )

4 = 0

X belongs to the empty set

( X-3 )

X-3 = 0 // + 3

X = 3

( X-6 )

X-6 = 0 // + 6

X = 6

X in { 3, 6 }