120^2+50^2=e^2

Solution for 120^2+50^2=e^2 equation:

120^2+50^2=e^2

We move all terms to the left:

120^2+50^2-(e^2)=0

We add all the numbers together, and all the variables

-1e^2+16900=0

a = -1; b = 0; c = +16900;
Δ = b2-4ac
Δ = 02-4·(-1)·16900
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-260}{2*-1}=\frac{-260}{-2}
=+130
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+260}{2*-1}=\frac{260}{-2}
=-130
$