14^2+15^2=x^2

Solution for 14^2+15^2=x^2 equation:

14^2+15^2=x^2

We move all terms to the left:

14^2+15^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+421=0

a = -1; b = 0; c = +421;
Δ = b2-4ac
Δ = 02-4·(-1)·421
Δ = 1684
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:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{421}}{2*-1}=\frac{0-2\sqrt{421}}{-2}
=-\frac{2\sqrt{421}}{-2}
=-\frac{\sqrt{421}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{421}}{2*-1}=\frac{0+2\sqrt{421}}{-2}
=\frac{2\sqrt{421}}{-2}
=\frac{\sqrt{421}}{-1}
$