Y=-0.01x^2+0.38x

Solution for Y=-0.01x^2+0.38x equation:

=-0.01Y^2+0.38Y

We move all terms to the left:

-(-0.01Y^2+0.38Y)=0

We get rid of parentheses

0.01Y^2-0.38Y=0

a = 0.01; b = -0.38; c = 0;
Δ = b2-4ac
Δ = -0.382-4·0.01·0
Δ = 0.1444
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{-(-0.38)-\sqrt{0.1444}}{2*0.01}=\frac{0.38-\sqrt{0.1444}}{0.02}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.38)+\sqrt{0.1444}}{2*0.01}=\frac{0.38+\sqrt{0.1444}}{0.02}
$