35^2+35^2=c^2

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

35^2+35^2=c^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1c^2+2450=0

a = -1; b = 0; c = +2450;
Δ = b2-4ac
Δ = 02-4·(-1)·2450
Δ = 9800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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