a^2+a^2=180^2

Solution for a^2+a^2=180^2 equation:

a^2+a^2=180^2

We move all terms to the left:

a^2+a^2-(180^2)=0

We add all the numbers together, and all the variables

2a^2-32400=0

a = 2; b = 0; c = -32400;
Δ = b2-4ac
Δ = 02-4·2·(-32400)
Δ = 259200
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:

$\sqrt{\Delta}=\sqrt{259200}=\sqrt{129600*2}=\sqrt{129600}*\sqrt{2}=360\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-360\sqrt{2}}{2*2}=\frac{0-360\sqrt{2}}{4}
=-\frac{360\sqrt{2}}{4}
=-90\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+360\sqrt{2}}{2*2}=\frac{0+360\sqrt{2}}{4}
=\frac{360\sqrt{2}}{4}
=90\sqrt{2}
$