a^2+2a^2=400^2

Solution for a^2+2a^2=400^2 equation:

a^2+2a^2=400^2

We move all terms to the left:

a^2+2a^2-(400^2)=0

We add all the numbers together, and all the variables

3a^2-160000=0

a = 3; b = 0; c = -160000;
Δ = b2-4ac
Δ = 02-4·3·(-160000)
Δ = 1920000
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:

$\sqrt{\Delta}=\sqrt{1920000}=\sqrt{640000*3}=\sqrt{640000}*\sqrt{3}=800\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{3}}{2*3}=\frac{0-800\sqrt{3}}{6}
=-\frac{800\sqrt{3}}{6}
=-\frac{400\sqrt{3}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{3}}{2*3}=\frac{0+800\sqrt{3}}{6}
=\frac{800\sqrt{3}}{6}
=\frac{400\sqrt{3}}{3}
$