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x in (-oo:+oo)
a = (12*x+24)*((1/2)*x+4) // - (12*x+24)*((1/2)*x+4)
a-((12*x+24)*((1/2)*x+4)) = 0
a-1*(12*x+24)*(1/2*x+4) = 0
a-1*(12*x+24)*(1/2*x+4) = 0
a-6*x^2-60*x-96 = 0
a-6*x^2-60*x-96 = 0
a-6*x^2-60*x-96 = 0
DELTA = (-60)^2-(-6*4*(a-96))
DELTA = 24*(a-96)+3600
24*(a-96)+3600 = 0
24*(a-96)+3600 = 0
24*a+1296 = 0
24*a+1296 = 0
24*a+1296 = 0 // - 1296
24*a = -1296 // : 24
a = -1296/24
a = -54
DELTA = 0 <=> t_3 = -54
x = 60/(-6*2) i a = -54
x = -5 i a = -54
( x = ((24*(a-96)+3600)^(1/2)+60)/(-6*2) or x = (60-(24*(a-96)+3600)^(1/2))/(-6*2) ) i a > -54
( x = ((24*(a-96)+3600)^(1/2)+60)/(-12) or x = (60-(24*(a-96)+3600)^(1/2))/(-12) ) i a > -54
a+54 > 0
a+54 > 0 // - 54
a > -54
x in { -5, ((24*(a-96)+3600)^(1/2)+60)/(-12), (60-(24*(a-96)+3600)^(1/2))/(-12) }
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