0=128-120x-x^2

Solution for 0=128-120x-x^2 equation:

0=128-120x-x^2

We move all terms to the left:

0-(128-120x-x^2)=0

We add all the numbers together, and all the variables

-(128-120x-x^2)=0

We get rid of parentheses

x^2+120x-128=0

a = 1; b = 120; c = -128;
Δ = b2-4ac
Δ = 1202-4·1·(-128)
Δ = 14912
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:

$\sqrt{\Delta}=\sqrt{14912}=\sqrt{64*233}=\sqrt{64}*\sqrt{233}=8\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{233}}{2*1}=\frac{-120-8\sqrt{233}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{233}}{2*1}=\frac{-120+8\sqrt{233}}{2}
$