0.05=0.02x-0.0002x^2

Solution for 0.05=0.02x-0.0002x^2 equation:

0.05=0.02x-0.0002x^2

We move all terms to the left:

0.05-(0.02x-0.0002x^2)=0

We get rid of parentheses

0.0002x^2-0.02x+0.05=0

a = 0.0002; b = -0.02; c = +0.05;
Δ = b2-4ac
Δ = -0.022-4·0.0002·0.05
Δ = 0.00036
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{-(-0.02)-\sqrt{0.00036}}{2*0.0002}=\frac{0.02-\sqrt{0.00036}}{0.0004}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.02)+\sqrt{0.00036}}{2*0.0002}=\frac{0.02+\sqrt{0.00036}}{0.0004}
$