a^2+a^2=315^2

Solution for a^2+a^2=315^2 equation:

a^2+a^2=315^2

We move all terms to the left:

a^2+a^2-(315^2)=0

We add all the numbers together, and all the variables

2a^2-99225=0

a = 2; b = 0; c = -99225;
Δ = b2-4ac
Δ = 02-4·2·(-99225)
Δ = 793800
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:

$\sqrt{\Delta}=\sqrt{793800}=\sqrt{396900*2}=\sqrt{396900}*\sqrt{2}=630\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-630\sqrt{2}}{2*2}=\frac{0-630\sqrt{2}}{4}
=-\frac{630\sqrt{2}}{4}
=-\frac{315\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+630\sqrt{2}}{2*2}=\frac{0+630\sqrt{2}}{4}
=\frac{630\sqrt{2}}{4}
=\frac{315\sqrt{2}}{2}
$