a^2+120^2=150^2

Solution for a^2+120^2=150^2 equation:

a^2+120^2=150^2

We move all terms to the left:

a^2+120^2-(150^2)=0

We add all the numbers together, and all the variables

a^2-8100=0

a = 1; b = 0; c = -8100;
Δ = b2-4ac
Δ = 02-4·1·(-8100)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180}{2*1}=\frac{-180}{2}
=-90
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180}{2*1}=\frac{180}{2}
=90
$