31^2+x^2=481^2

Solution for 31^2+x^2=481^2 equation:

31^2+x^2=481^2

We move all terms to the left:

31^2+x^2-(481^2)=0

We add all the numbers together, and all the variables

x^2-230400=0

a = 1; b = 0; c = -230400;
Δ = b2-4ac
Δ = 02-4·1·(-230400)
Δ = 921600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{921600}=960$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-960}{2*1}=\frac{-960}{2}
=-480
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+960}{2*1}=\frac{960}{2}
=480
$