0=120x-x^2-240

Solution for 0=120x-x^2-240 equation:

0=120x-x^2-240

We move all terms to the left:

0-(120x-x^2-240)=0

We add all the numbers together, and all the variables

-(120x-x^2-240)=0

We get rid of parentheses

x^2-120x+240=0

a = 1; b = -120; c = +240;
Δ = b2-4ac
Δ = -1202-4·1·240
Δ = 13440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13440}=\sqrt{64*210}=\sqrt{64}*\sqrt{210}=8\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{210}}{2*1}=\frac{120-8\sqrt{210}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{210}}{2*1}=\frac{120+8\sqrt{210}}{2}
$