7^2+7^2=c^2

Solution for 7^2+7^2=c^2 equation:

7^2+7^2=c^2

We move all terms to the left:

7^2+7^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+98=0

a = -1; b = 0; c = +98;
Δ = b2-4ac
Δ = 02-4·(-1)·98
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*-1}=\frac{0-14\sqrt{2}}{-2}
=-\frac{14\sqrt{2}}{-2}
=-\frac{7\sqrt{2}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*-1}=\frac{0+14\sqrt{2}}{-2}
=\frac{14\sqrt{2}}{-2}
=\frac{7\sqrt{2}}{-1}
$