6=(1/9)(8*((6+a)/2)*(((6+a)/2)-1))

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Solution for 6=(1/9)(8*((6+a)/2)*(((6+a)/2)-1)) equation: 


a in (-oo:+oo)

6 = 8*(1/9)*((a+6)/2)*((a+6)/2-1) // - 8*(1/9)*((a+6)/2)*((a+6)/2-1)

6-(8*(1/9)*((a+6)/2)*((a+6)/2-1)) = 0

(-4/9)*((a+6)/2-1)*(a+6)+6 = 0

6-4/9*(a+6)*((a+6)/2-1) = 0

6-4/9*(a+6)*((a+6)/2-1) = 0

2/3-2/9*a^2-20/9*a = 0

2/3-2/9*a^2-20/9*a = 0

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

1-1/3*a^2-10/3*a = 0

DELTA = (-10/3)^2-(-1/3*1*4)

DELTA = 112/9

DELTA > 0

a = ((112/9)^(1/2)+10/3)/(-1/3*2) or a = (10/3-(112/9)^(1/2))/(-1/3*2)

a = -3/2*((112/9)^(1/2)+10/3) or a = -3/2*(10/3-(112/9)^(1/2))

2/3*(a+3/2*((112/9)^(1/2)+10/3))*(a+3/2*(10/3-(112/9)^(1/2))) = 0

2/3*(a+3/2*((112/9)^(1/2)+10/3))*(a+3/2*(10/3-(112/9)^(1/2))) = 0

( a+3/2*((112/9)^(1/2)+10/3) )

a+3/2*((112/9)^(1/2)+10/3) = 0 // - 3/2*((112/9)^(1/2)+10/3)

a = -(3/2*((112/9)^(1/2)+10/3))

a = -3/2*((112/9)^(1/2)+10/3)

( a+3/2*(10/3-(112/9)^(1/2)) )

a+3/2*(10/3-(112/9)^(1/2)) = 0 // - 3/2*(10/3-(112/9)^(1/2))

a = -(3/2*(10/3-(112/9)^(1/2)))

a = -3/2*(10/3-(112/9)^(1/2))

a in { -3/2*((112/9)^(1/2)+10/3), -3/2*(10/3-(112/9)^(1/2)) }

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