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

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


x in (-oo:+oo)

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

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

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

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

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

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

10*x^2-10*x+3/2 = 0

10*x^2-10*x+3/2 = 0

10*x^2-10*x+3/2 = 0

DELTA = (-10)^2-(3/2*4*10)

DELTA = 40

DELTA > 0

x = (40^(1/2)+10)/(2*10) or x = (10-40^(1/2))/(2*10)

x = (2*10^(1/2)+10)/20 or x = (10-2*10^(1/2))/20

(x-((10-2*10^(1/2))/20))*(x-((2*10^(1/2)+10)/20)) = 0

((x-((10-2*10^(1/2))/20))*(x-((2*10^(1/2)+10)/20)))/5 = 0

((x-((10-2*10^(1/2))/20))*(x-((2*10^(1/2)+10)/20)))/5 = 0 // * 5

(x-((10-2*10^(1/2))/20))*(x-((2*10^(1/2)+10)/20)) = 0

( x-((10-2*10^(1/2))/20) )

x-((10-2*10^(1/2))/20) = 0 // + (10-2*10^(1/2))/20

x = (10-2*10^(1/2))/20

( x-((2*10^(1/2)+10)/20) )

x-((2*10^(1/2)+10)/20) = 0 // + (2*10^(1/2)+10)/20

x = (2*10^(1/2)+10)/20

x in { (10-2*10^(1/2))/20, (2*10^(1/2)+10)/20 }

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