Y=100+0,8q-0,02q^2

Solution for Y=100+0,8q-0,02q^2 equation:

=100+0.8Y-0.02Y^2

We move all terms to the left:

-(100+0.8Y-0.02Y^2)=0

We get rid of parentheses

0.02Y^2-0.8Y-100=0

a = 0.02; b = -0.8; c = -100;
Δ = b2-4ac
Δ = -0.82-4·0.02·(-100)
Δ = 8.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.8)-\sqrt{8.64}}{2*0.02}=\frac{0.8-\sqrt{8.64}}{0.04}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{8.64}}{2*0.02}=\frac{0.8+\sqrt{8.64}}{0.04}
$