50^2+x^2=260^2

Solution for 50^2+x^2=260^2 equation:

50^2+x^2=260^2

We move all terms to the left:

50^2+x^2-(260^2)=0

We add all the numbers together, and all the variables

x^2-65100=0

a = 1; b = 0; c = -65100;
Δ = b2-4ac
Δ = 02-4·1·(-65100)
Δ = 260400
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:

$\sqrt{\Delta}=\sqrt{260400}=\sqrt{400*651}=\sqrt{400}*\sqrt{651}=20\sqrt{651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{651}}{2*1}=\frac{0-20\sqrt{651}}{2}
=-\frac{20\sqrt{651}}{2}
=-10\sqrt{651}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{651}}{2*1}=\frac{0+20\sqrt{651}}{2}
=\frac{20\sqrt{651}}{2}
=10\sqrt{651}
$