120+x*x=520

Solution for 120+x*x=520 equation:

120+x*x=520

We move all terms to the left:

120+x*x-(520)=0

We add all the numbers together, and all the variables

x*x-400=0

Wy multiply elements

x^2-400=0

a = 1; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·1·(-400)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*1}=\frac{40}{2}
=20
$