800-x=x^2+380

Solution for 800-x=x^2+380 equation:

800-x=x^2+380

We move all terms to the left:

800-x-(x^2+380)=0

We add all the numbers together, and all the variables

-1x-(x^2+380)+800=0

We get rid of parentheses

-x^2-1x-380+800=0

We add all the numbers together, and all the variables

-1x^2-1x+420=0

a = -1; b = -1; c = +420;
Δ = b2-4ac
Δ = -12-4·(-1)·420
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*-1}=\frac{42}{-2}
=-21
$