45^2+80^2=c^2

Solution for 45^2+80^2=c^2 equation:

45^2+80^2=c^2

We move all terms to the left:

45^2+80^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+8425=0

a = -1; b = 0; c = +8425;
Δ = b2-4ac
Δ = 02-4·(-1)·8425
Δ = 33700
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:

$\sqrt{\Delta}=\sqrt{33700}=\sqrt{100*337}=\sqrt{100}*\sqrt{337}=10\sqrt{337}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{337}}{2*-1}=\frac{0-10\sqrt{337}}{-2}
=-\frac{10\sqrt{337}}{-2}
=-\frac{5\sqrt{337}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{337}}{2*-1}=\frac{0+10\sqrt{337}}{-2}
=\frac{10\sqrt{337}}{-2}
=\frac{5\sqrt{337}}{-1}
$