a^2+a^2=200^2

Solution for a^2+a^2=200^2 equation:

a^2+a^2=200^2

We move all terms to the left:

a^2+a^2-(200^2)=0

We add all the numbers together, and all the variables

2a^2-40000=0

a = 2; b = 0; c = -40000;
Δ = b2-4ac
Δ = 02-4·2·(-40000)
Δ = 320000
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:

$\sqrt{\Delta}=\sqrt{320000}=\sqrt{160000*2}=\sqrt{160000}*\sqrt{2}=400\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{2}}{2*2}=\frac{0-400\sqrt{2}}{4}
=-\frac{400\sqrt{2}}{4}
=-100\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{2}}{2*2}=\frac{0+400\sqrt{2}}{4}
=\frac{400\sqrt{2}}{4}
=100\sqrt{2}
$