x-x^2=-782000

Solution for x-x^2=-782000 equation:

x-x^2=-782000

We move all terms to the left:

x-x^2-(-782000)=0

We add all the numbers together, and all the variables

-1x^2+x+782000=0

a = -1; b = 1; c = +782000;
Δ = b2-4ac
Δ = 12-4·(-1)·782000
Δ = 3128001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{3128001}}{2*-1}=\frac{-1-\sqrt{3128001}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3128001}}{2*-1}=\frac{-1+\sqrt{3128001}}{-2}
$