-x^2+420x-8000=0

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

-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 = 144400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144400}=380$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-380}{2*-1}=\frac{-800}{-2}
=+400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+380}{2*-1}=\frac{-40}{-2}
=+20
$