(1/8)(x-3)^2=5

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Solution for (1/8)(x-3)^2=5 equation: 


x in (-oo:+oo)

(1/8)*(x-3)^2 = 5 // - 5

(1/8)*(x-3)^2-5 = 0

1/8*(x-3)^2-5 = 0

1/8*(x-3)^2-5 = 0

1/8*x^2-3/4*x-31/8 = 0

1/8*x^2-3/4*x-31/8 = 0

1/4*(1/2*x^2-3*x-31/2) = 0

1/2*x^2-3*x-31/2 = 0

DELTA = (-3)^2-(-31/2*1/2*4)

DELTA = 40

DELTA > 0

x = (40^(1/2)+3)/(1/2*2) or x = (3-40^(1/2))/(1/2*2)

x = 2*10^(1/2)+3 or x = 3-2*10^(1/2)

1/4*(x+2*10^(1/2)-3)*(x-2*10^(1/2)-3) = 0

1/4*(x+2*10^(1/2)-3)*(x-2*10^(1/2)-3) = 0

( x+2*10^(1/2)-3 )

x+2*10^(1/2)-3 = 0 // - 2*10^(1/2)-3

x = -(2*10^(1/2)-3)

x = 3-(2*10^(1/2))

( x-2*10^(1/2)-3 )

x-2*10^(1/2)-3 = 0 // + -2*10^(1/2)-3

x = -(-2*10^(1/2)-3)

x = 3-(-2*10^(1/2))

x in { 3-(2*10^(1/2)), 3-(-2*10^(1/2)) }

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