90^2+120^2=x^2

Solution for 90^2+120^2=x^2 equation:

90^2+120^2=x^2

We move all terms to the left:

90^2+120^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+22500=0

a = -1; b = 0; c = +22500;
Δ = b2-4ac
Δ = 02-4·(-1)·22500
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300}{2*-1}=\frac{-300}{-2}
=+150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300}{2*-1}=\frac{300}{-2}
=-150
$