0=-2x^2+1000x-80000

Solution for 0=-2x^2+1000x-80000 equation:

0=-2x^2+1000x-80000

We move all terms to the left:

0-(-2x^2+1000x-80000)=0

We add all the numbers together, and all the variables

-(-2x^2+1000x-80000)=0

We get rid of parentheses

2x^2-1000x+80000=0

a = 2; b = -1000; c = +80000;
Δ = b2-4ac
Δ = -10002-4·2·80000
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-600}{2*2}=\frac{400}{4}
=100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+600}{2*2}=\frac{1600}{4}
=400
$