x=-1/12(x+5)^2+1

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Solution for x=-1/12(x+5)^2+1 equation: 


x in (-oo:+oo)

x = (-1/12)*(x+5)^2+1 // - (-1/12)*(x+5)^2+1

x-((-1/12)*(x+5)^2)-1 = 0

(1/12)*(x+5)^2+x-1 = 0

1/12*(x+5)^2+x-1 = 0

1/12*(x+5)^2+x-1 = 0

1/12*x^2+11/6*x-1+25/12 = 0

1/12*x^2+11/6*x+13/12 = 0

1/12*x^2+11/6*x+13/12 = 0

1/6*(1/2*x^2+11*x+13/2) = 0

1/2*x^2+11*x+13/2 = 0

DELTA = 11^2-(1/2*4*13/2)

DELTA = 108

DELTA > 0

x = (108^(1/2)-11)/(1/2*2) or x = (-108^(1/2)-11)/(1/2*2)

x = 6*3^(1/2)-11 or x = -6*3^(1/2)-11

1/6*(x+6*3^(1/2)+11)*(x-6*3^(1/2)+11) = 0

1/6*(x+6*3^(1/2)+11)*(x-6*3^(1/2)+11) = 0

( x+6*3^(1/2)+11 )

x+6*3^(1/2)+11 = 0 // - 6*3^(1/2)+11

x = -(6*3^(1/2)+11)

( x-6*3^(1/2)+11 )

x-6*3^(1/2)+11 = 0 // - 11-6*3^(1/2)

x = -(11-6*3^(1/2))

x in { -(6*3^(1/2)+11), -(11-6*3^(1/2)) }

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