q^2-40q+200=0

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

q^2-40q+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:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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