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)=0

We add all the numbers together, and all the variables

a^2-14400=0

a = 1; b = 0; c = -14400;
Δ = b2-4ac
Δ = 02-4·1·(-14400)
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240}{2*1}=\frac{-240}{2}
=-120
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240}{2*1}=\frac{240}{2}
=120
$