2*(a^2)=(576^2)

Solution for 2*(a^2)=(576^2) equation:

2(a^2)=(576^2)

We move all terms to the left:

2(a^2)-((576^2))=0

determiningTheFunctionDomain
2a^2-576^2=0

We add all the numbers together, and all the variables

2a^2-331776=0

a = 2; b = 0; c = -331776;
Δ = b2-4ac
Δ = 02-4·2·(-331776)
Δ = 2654208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2654208}=\sqrt{1327104*2}=\sqrt{1327104}*\sqrt{2}=1152\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1152\sqrt{2}}{2*2}=\frac{0-1152\sqrt{2}}{4}
=-\frac{1152\sqrt{2}}{4}
=-288\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1152\sqrt{2}}{2*2}=\frac{0+1152\sqrt{2}}{4}
=\frac{1152\sqrt{2}}{4}
=288\sqrt{2}
$