x*x-40x-200=0

Solution for x*x-40x-200=0 equation:

x*x-40x-200=0

We add all the numbers together, and all the variables

-40x+x*x-200=0

Wy multiply elements

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

The end solution:

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