100-0.2x=0.001x^2

Solution for 100-0.2x=0.001x^2 equation:

100-0.2x=0.001x^2

We move all terms to the left:

100-0.2x-(0.001x^2)=0

We get rid of parentheses

-0.001x^2-0.2x+100=0

a = -0.001; b = -0.2; c = +100;
Δ = b2-4ac
Δ = -0.22-4·(-0.001)·100
Δ = 0.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-\sqrt{0.44}}{2*-0.001}=\frac{0.2-\sqrt{0.44}}{-0.002}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{0.44}}{2*-0.001}=\frac{0.2+\sqrt{0.44}}{-0.002}
$