24a^2-11*96a+96*96=0

Solution for 24a^2-11*96a+96*96=0 equation:

24a^2-11*96a+96*96=0

We add all the numbers together, and all the variables

24a^2-11*96a+9216=0

Wy multiply elements

24a^2-1056a+9216=0

a = 24; b = -1056; c = +9216;
Δ = b2-4ac
Δ = -10562-4·24·9216
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1056)-480}{2*24}=\frac{576}{48}
=12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1056)+480}{2*24}=\frac{1536}{48}
=32
$