(X-3/2)^2=7/4

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Solution for (X-3/2)^2=7/4 equation: 


X in (-oo:+oo)

(X-(3/2))^2 = 7/4 // - 7/4

(X-(3/2))^2-(7/4) = 0

(X-3/2)^2-7/4 = 0

(4*(X-3/2)^2)/4-7/4 = 0

4*(X-3/2)^2-7 = 0

4*X^2-12*X+2 = 0

4*X^2-12*X+2 = 0

2*(2*X^2-6*X+1) = 0

2*X^2-6*X+1 = 0

DELTA = (-6)^2-(1*2*4)

DELTA = 28

DELTA > 0

X = (28^(1/2)+6)/(2*2) or X = (6-28^(1/2))/(2*2)

X = (2*7^(1/2)+6)/4 or X = (6-2*7^(1/2))/4

2*(X-((6-2*7^(1/2))/4))*(X-((2*7^(1/2)+6)/4)) = 0

(2*(X-((6-2*7^(1/2))/4))*(X-((2*7^(1/2)+6)/4)))/4 = 0

(2*(X-((6-2*7^(1/2))/4))*(X-((2*7^(1/2)+6)/4)))/4 = 0 // * 4

2*(X-((6-2*7^(1/2))/4))*(X-((2*7^(1/2)+6)/4)) = 0

( 2 )

2 = 0

X belongs to the empty set

( X-((2*7^(1/2)+6)/4) )

X-((2*7^(1/2)+6)/4) = 0 // + (2*7^(1/2)+6)/4

X = (2*7^(1/2)+6)/4

( X-((6-2*7^(1/2))/4) )

X-((6-2*7^(1/2))/4) = 0 // + (6-2*7^(1/2))/4

X = (6-2*7^(1/2))/4

X in { (2*7^(1/2)+6)/4, (6-2*7^(1/2))/4 }

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