40x-x^2-100=0

Solution for 40x-x^2-100=0 equation:

40x-x^2-100=0

We add all the numbers together, and all the variables

-1x^2+40x-100=0

a = -1; b = 40; c = -100;
Δ = b2-4ac
Δ = 402-4·(-1)·(-100)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{3}}{2*-1}=\frac{-40-20\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{3}}{2*-1}=\frac{-40+20\sqrt{3}}{-2}
$