0=2x^2+1000x-800000

Solution for 0=2x^2+1000x-800000 equation:

0=2x^2+1000x-800000

We move all terms to the left:

0-(2x^2+1000x-800000)=0

We add all the numbers together, and all the variables

-(2x^2+1000x-800000)=0

We get rid of parentheses

-2x^2-1000x+800000=0

a = -2; b = -1000; c = +800000;
Δ = b2-4ac
Δ = -10002-4·(-2)·800000
Δ = 7400000
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:

$\sqrt{\Delta}=\sqrt{7400000}=\sqrt{40000*185}=\sqrt{40000}*\sqrt{185}=200\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-200\sqrt{185}}{2*-2}=\frac{1000-200\sqrt{185}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+200\sqrt{185}}{2*-2}=\frac{1000+200\sqrt{185}}{-4}
$