100=x+.0002x^2

Solution for 100=x+.0002x^2 equation:

100=x+.0002x^2

We move all terms to the left:

100-(x+.0002x^2)=0

We get rid of parentheses

-.0002x^2-x+100=0

We add all the numbers together, and all the variables

-0.0002x^2-1x+100=0

a = -0.0002; b = -1; c = +100;
Δ = b2-4ac
Δ = -12-4·(-0.0002)·100
Δ = 1.08
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{-(-1)-\sqrt{1.08}}{2*-0.0002}=\frac{1-\sqrt{1.08}}{-0.0004}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.08}}{2*-0.0002}=\frac{1+\sqrt{1.08}}{-0.0004}
$