1/2(x-1)^2-3=9

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Solution for 1/2(x-1)^2-3=9 equation: 


x in (-oo:+oo)

(1/2)*(x-1)^2-3 = 9 // - 9

(1/2)*(x-1)^2-9-3 = 0

1/2*(x-1)^2-9-3 = 0

1/2*(x-1)^2-9-3 = 0

1/2*x^2-x-17/2-3 = 0

1/2*x^2-x-23/2 = 0

1/2*x^2-x-23/2 = 0

1/2*x^2-x-23/2 = 0

DELTA = (-1)^2-(-23/2*1/2*4)

DELTA = 24

DELTA > 0

x = (24^(1/2)+1)/(1/2*2) or x = (1-24^(1/2))/(1/2*2)

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

(x+2*6^(1/2)-1)*(x-2*6^(1/2)-1) = 0

(x+2*6^(1/2)-1)*(x-2*6^(1/2)-1) = 0

( x+2*6^(1/2)-1 )

x+2*6^(1/2)-1 = 0 // - 2*6^(1/2)-1

x = -(2*6^(1/2)-1)

x = 1-(2*6^(1/2))

( x-2*6^(1/2)-1 )

x-2*6^(1/2)-1 = 0 // + -2*6^(1/2)-1

x = -(-2*6^(1/2)-1)

x = 1-(-2*6^(1/2))

x in { 1-(2*6^(1/2)), 1-(-2*6^(1/2)) }

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