200-100x-x^2=0

Solution for 200-100x-x^2=0 equation:

200-100x-x^2=0

We add all the numbers together, and all the variables

-1x^2-100x+200=0

a = -1; b = -100; c = +200;
Δ = b2-4ac
Δ = -1002-4·(-1)·200
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{3}}{2*-1}=\frac{100-60\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{3}}{2*-1}=\frac{100+60\sqrt{3}}{-2}
$