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

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Solution for 5(x-1/2)^2=13/4 equation: 


x in (-oo:+oo)

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

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

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

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

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

20*x^2-20*x-8 = 0

20*x^2-20*x-8 = 0

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

5*x^2-5*x-2 = 0

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

DELTA = 65

DELTA > 0

x = (65^(1/2)+5)/(2*5) or x = (5-65^(1/2))/(2*5)

x = (65^(1/2)+5)/10 or x = (5-65^(1/2))/10

4*(x-((5-65^(1/2))/10))*(x-((65^(1/2)+5)/10)) = 0

(4*(x-((5-65^(1/2))/10))*(x-((65^(1/2)+5)/10)))/4 = 0

(4*(x-((5-65^(1/2))/10))*(x-((65^(1/2)+5)/10)))/4 = 0 // * 4

4*(x-((5-65^(1/2))/10))*(x-((65^(1/2)+5)/10)) = 0

( 4 )

4 = 0

x belongs to the empty set

( x-((5-65^(1/2))/10) )

x-((5-65^(1/2))/10) = 0 // + (5-65^(1/2))/10

x = (5-65^(1/2))/10

( x-((65^(1/2)+5)/10) )

x-((65^(1/2)+5)/10) = 0 // + (65^(1/2)+5)/10

x = (65^(1/2)+5)/10

x in { (5-65^(1/2))/10, (65^(1/2)+5)/10 }

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