-s^2+40s+200=0

Solution for -s^2+40s+200=0 equation:

-s^2+40s+200=0

We add all the numbers together, and all the variables

-1s^2+40s+200=0

a = -1; b = 40; c = +200;
Δ = b2-4ac
Δ = 402-4·(-1)·200
Δ = 2400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{6}}{2*-1}=\frac{-40-20\sqrt{6}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{6}}{2*-1}=\frac{-40+20\sqrt{6}}{-2}
$