0=x^2+40x+200

Solution for 0=x^2+40x+200 equation:

0=x^2+40x+200

We move all terms to the left:

0-(x^2+40x+200)=0

We add all the numbers together, and all the variables

-(x^2+40x+200)=0

We get rid of parentheses

-x^2-40x-200=0

We add all the numbers together, and all the variables

-1x^2-40x-200=0

a = -1; b = -40; c = -200;
Δ = b2-4ac
Δ = -402-4·(-1)·(-200)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{2}}{2*-1}=\frac{40-20\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{2}}{2*-1}=\frac{40+20\sqrt{2}}{-2}
$