0=5x^2-120x-1000

Solution for 0=5x^2-120x-1000 equation:

0=5x^2-120x-1000

We move all terms to the left:

0-(5x^2-120x-1000)=0

We add all the numbers together, and all the variables

-(5x^2-120x-1000)=0

We get rid of parentheses

-5x^2+120x+1000=0

a = -5; b = 120; c = +1000;
Δ = b2-4ac
Δ = 1202-4·(-5)·1000
Δ = 34400
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:

$\sqrt{\Delta}=\sqrt{34400}=\sqrt{400*86}=\sqrt{400}*\sqrt{86}=20\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{86}}{2*-5}=\frac{-120-20\sqrt{86}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{86}}{2*-5}=\frac{-120+20\sqrt{86}}{-10}
$