800x=-x^2

Solution for 800x=-x^2 equation:

800x=-x^2

We move all terms to the left:

800x-(-x^2)=0

We get rid of parentheses

x^2+800x=0

a = 1; b = 800; c = 0;
Δ = b2-4ac
Δ = 8002-4·1·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(800)-800}{2*1}=\frac{-1600}{2}
=-800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(800)+800}{2*1}=\frac{0}{2}
=0
$