a^2+120^2=250^2

Solution for a^2+120^2=250^2 equation:

a^2+120^2=250^2

We move all terms to the left:

a^2+120^2-(250^2)=0

We add all the numbers together, and all the variables

a^2-48100=0

a = 1; b = 0; c = -48100;
Δ = b2-4ac
Δ = 02-4·1·(-48100)
Δ = 192400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192400}=\sqrt{400*481}=\sqrt{400}*\sqrt{481}=20\sqrt{481}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{481}}{2*1}=\frac{0-20\sqrt{481}}{2}
=-\frac{20\sqrt{481}}{2}
=-10\sqrt{481}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{481}}{2*1}=\frac{0+20\sqrt{481}}{2}
=\frac{20\sqrt{481}}{2}
=10\sqrt{481}
$