31^2+x^2=39^2

Solution for 31^2+x^2=39^2 equation:

31^2+x^2=39^2

We move all terms to the left:

31^2+x^2-(39^2)=0

We add all the numbers together, and all the variables

x^2-560=0

a = 1; b = 0; c = -560;
Δ = b2-4ac
Δ = 02-4·1·(-560)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*1}=\frac{0-8\sqrt{35}}{2}
=-\frac{8\sqrt{35}}{2}
=-4\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*1}=\frac{0+8\sqrt{35}}{2}
=\frac{8\sqrt{35}}{2}
=4\sqrt{35}
$