0=x^2-120x-160800

Solution for 0=x^2-120x-160800 equation:

0=x^2-120x-160800

We move all terms to the left:

0-(x^2-120x-160800)=0

We add all the numbers together, and all the variables

-(x^2-120x-160800)=0

We get rid of parentheses

-x^2+120x+160800=0

We add all the numbers together, and all the variables

-1x^2+120x+160800=0

a = -1; b = 120; c = +160800;
Δ = b2-4ac
Δ = 1202-4·(-1)·160800
Δ = 657600
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:

$\sqrt{\Delta}=\sqrt{657600}=\sqrt{1600*411}=\sqrt{1600}*\sqrt{411}=40\sqrt{411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{411}}{2*-1}=\frac{-120-40\sqrt{411}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{411}}{2*-1}=\frac{-120+40\sqrt{411}}{-2}
$