0=x^2-420x-8000

Solution for 0=x^2-420x-8000 equation:

0=x^2-420x-8000

We move all terms to the left:

0-(x^2-420x-8000)=0

We add all the numbers together, and all the variables

-(x^2-420x-8000)=0

We get rid of parentheses

-x^2+420x+8000=0

We add all the numbers together, and all the variables

-1x^2+420x+8000=0

a = -1; b = 420; c = +8000;
Δ = b2-4ac
Δ = 4202-4·(-1)·8000
Δ = 208400
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:

$\sqrt{\Delta}=\sqrt{208400}=\sqrt{400*521}=\sqrt{400}*\sqrt{521}=20\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-20\sqrt{521}}{2*-1}=\frac{-420-20\sqrt{521}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+20\sqrt{521}}{2*-1}=\frac{-420+20\sqrt{521}}{-2}
$