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

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


x in (-oo:+oo)

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

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

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

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

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

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

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

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

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

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

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

DELTA = 120

DELTA > 0

x = (120^(1/2)-11)/(1/2*2) or x = (-120^(1/2)-11)/(1/2*2)

x = 2*30^(1/2)-11 or x = -2*30^(1/2)-11

1/6*(x+2*30^(1/2)+11)*(x-2*30^(1/2)+11) = 0

1/6*(x+2*30^(1/2)+11)*(x-2*30^(1/2)+11) = 0

( x+2*30^(1/2)+11 )

x+2*30^(1/2)+11 = 0 // - 2*30^(1/2)+11

x = -(2*30^(1/2)+11)

( x-2*30^(1/2)+11 )

x-2*30^(1/2)+11 = 0 // - 11-2*30^(1/2)

x = -(11-2*30^(1/2))

x in { -(2*30^(1/2)+11), -(11-2*30^(1/2)) }

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