G(x)=0.5x-0.002x^2

Solution for G(x)=0.5x-0.002x^2 equation:

(G)=0.5G-0.002G^2

We move all terms to the left:

(G)-(0.5G-0.002G^2)=0

We get rid of parentheses

0.002G^2-0.5G+G=0

We add all the numbers together, and all the variables

0.002G^2+0.5G=0

a = 0.002; b = 0.5; c = 0;
Δ = b2-4ac
Δ = 0.52-4·0.002·0
Δ = 0.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.5)-\sqrt{0.25}}{2*0.002}=\frac{-0.5-\sqrt{0.25}}{0.004}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{0.25}}{2*0.002}=\frac{-0.5+\sqrt{0.25}}{0.004}
$