a^2+a^2=35^2

Solution for a^2+a^2=35^2 equation:

a^2+a^2=35^2

We move all terms to the left:

a^2+a^2-(35^2)=0

We add all the numbers together, and all the variables

2a^2-1225=0

a = 2; b = 0; c = -1225;
Δ = b2-4ac
Δ = 02-4·2·(-1225)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{2}}{2*2}=\frac{0-70\sqrt{2}}{4}
=-\frac{70\sqrt{2}}{4}
=-\frac{35\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{2}}{2*2}=\frac{0+70\sqrt{2}}{4}
=\frac{70\sqrt{2}}{4}
=\frac{35\sqrt{2}}{2}
$