x^2+80^2=200^2

Solution for x^2+80^2=200^2 equation:

x^2+80^2=200^2

We move all terms to the left:

x^2+80^2-(200^2)=0

We add all the numbers together, and all the variables

x^2-33600=0

a = 1; b = 0; c = -33600;
Δ = b2-4ac
Δ = 02-4·1·(-33600)
Δ = 134400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{134400}=\sqrt{6400*21}=\sqrt{6400}*\sqrt{21}=80\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{21}}{2*1}=\frac{0-80\sqrt{21}}{2}
=-\frac{80\sqrt{21}}{2}
=-40\sqrt{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{21}}{2*1}=\frac{0+80\sqrt{21}}{2}
=\frac{80\sqrt{21}}{2}
=40\sqrt{21}
$