168^2+x^2=360^2

Solution for 168^2+x^2=360^2 equation:

168^2+x^2=360^2

We move all terms to the left:

168^2+x^2-(360^2)=0

We add all the numbers together, and all the variables

x^2-101376=0

a = 1; b = 0; c = -101376;
Δ = b2-4ac
Δ = 02-4·1·(-101376)
Δ = 405504
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:

$\sqrt{\Delta}=\sqrt{405504}=\sqrt{36864*11}=\sqrt{36864}*\sqrt{11}=192\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-192\sqrt{11}}{2*1}=\frac{0-192\sqrt{11}}{2}
=-\frac{192\sqrt{11}}{2}
=-96\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+192\sqrt{11}}{2*1}=\frac{0+192\sqrt{11}}{2}
=\frac{192\sqrt{11}}{2}
=96\sqrt{11}
$