(x-5/2)^2=13/4

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Solution for (x-5/2)^2=13/4 equation: 


x in (-oo:+oo)

(x-(5/2))^2 = 13/4 // - 13/4

(x-(5/2))^2-(13/4) = 0

(x-5/2)^2-13/4 = 0

(4*(x-5/2)^2)/4-13/4 = 0

4*(x-5/2)^2-13 = 0

4*x^2-20*x+12 = 0

4*x^2-20*x+12 = 0

4*(x^2-5*x+3) = 0

x^2-5*x+3 = 0

DELTA = (-5)^2-(1*3*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)+5)/(1*2) or x = (5-13^(1/2))/(1*2)

x = (13^(1/2)+5)/2 or x = (5-13^(1/2))/2

4*(x-((5-13^(1/2))/2))*(x-((13^(1/2)+5)/2)) = 0

(4*(x-((5-13^(1/2))/2))*(x-((13^(1/2)+5)/2)))/4 = 0

(4*(x-((5-13^(1/2))/2))*(x-((13^(1/2)+5)/2)))/4 = 0 // * 4

4*(x-((5-13^(1/2))/2))*(x-((13^(1/2)+5)/2)) = 0

( 4 )

4 = 0

x belongs to the empty set

( x-((13^(1/2)+5)/2) )

x-((13^(1/2)+5)/2) = 0 // + (13^(1/2)+5)/2

x = (13^(1/2)+5)/2

( x-((5-13^(1/2))/2) )

x-((5-13^(1/2))/2) = 0 // + (5-13^(1/2))/2

x = (5-13^(1/2))/2

x in { (13^(1/2)+5)/2, (5-13^(1/2))/2 }

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