Question 293255
You did it correctly but you explained it wrong.
"Divide both sides by 8 and then you get"
You didn't divide, you actually multiplied.
You didn't really do this 1/2(8/3)^2
You really did this (4/3)^2 or (8/3*1/2)^2 which equals 16/9.
And you don't end up with x^2 + 8/3 - 1/3 = 0 but x^2 + 8x/3 - 1/3 = 0
You  forgot the x in the x term
BTW We didn't really need to get it equal to 0
x^2 + 8x/3 = 1/3 
So now we add 16/9
x^2 + 8x/3+16/9 = 1/3 +16/9
x^2 + 8x/3+16/9 = 3/9 +16/9
x^2 + 8x/3+16/9 = 19/9
(x+4/3)^2=19/9
x=-4/3+-sqrt(19/9)
x=-4/3+-sqrt(19/9)

x=1/3(-4-sqrt(19))
x=1/3(-4+sqrt(19))