x^2+14^2=31^2

Solution for x^2+14^2=31^2 equation:

x^2+14^2=31^2

We move all terms to the left:

x^2+14^2-(31^2)=0

We add all the numbers together, and all the variables

x^2-765=0

a = 1; b = 0; c = -765;
Δ = b2-4ac
Δ = 02-4·1·(-765)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{85}}{2*1}=\frac{0-6\sqrt{85}}{2}
=-\frac{6\sqrt{85}}{2}
=-3\sqrt{85}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{85}}{2*1}=\frac{0+6\sqrt{85}}{2}
=\frac{6\sqrt{85}}{2}
=3\sqrt{85}
$