Y=-0.1x^2+0.9x

Solution for Y=-0.1x^2+0.9x equation:

=-0.1Y^2+0.9Y

We move all terms to the left:

-(-0.1Y^2+0.9Y)=0

We get rid of parentheses

0.1Y^2-0.9Y=0

a = 0.1; b = -0.9; c = 0;
Δ = b2-4ac
Δ = -0.92-4·0.1·0
Δ = 0.81
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{-(-0.9)-\sqrt{0.81}}{2*0.1}=\frac{0.9-\sqrt{0.81}}{0.2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{0.81}}{2*0.1}=\frac{0.9+\sqrt{0.81}}{0.2}
$