70^2+42^2=c^2

Solution for 70^2+42^2=c^2 equation:

70^2+42^2=c^2

We move all terms to the left:

70^2+42^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+6664=0

a = -1; b = 0; c = +6664;
Δ = b2-4ac
Δ = 02-4·(-1)·6664
Δ = 26656
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:

$\sqrt{\Delta}=\sqrt{26656}=\sqrt{784*34}=\sqrt{784}*\sqrt{34}=28\sqrt{34}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{34}}{2*-1}=\frac{0-28\sqrt{34}}{-2}
=-\frac{28\sqrt{34}}{-2}
=-\frac{14\sqrt{34}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{34}}{2*-1}=\frac{0+28\sqrt{34}}{-2}
=\frac{28\sqrt{34}}{-2}
=\frac{14\sqrt{34}}{-1}
$