-x^2+100x-2000=0

Solution for -x^2+100x-2000=0 equation:

-x^2+100x-2000=0

We add all the numbers together, and all the variables

-1x^2+100x-2000=0

a = -1; b = 100; c = -2000;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2000)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{5}}{2*-1}=\frac{-100-20\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{5}}{2*-1}=\frac{-100+20\sqrt{5}}{-2}
$