380-x-x^2=0

Solution for 380-x-x^2=0 equation:

380-x-x^2=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +380;
Δ = b2-4ac
Δ = -12-4·(-1)·380
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-39}{2*-1}=\frac{-38}{-2}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+39}{2*-1}=\frac{40}{-2}
=-20
$