Y=-0.05x^2+x+1.5

Solution for Y=-0.05x^2+x+1.5 equation:

=-0.05Y^2+Y+1.5

We move all terms to the left:

-(-0.05Y^2+Y+1.5)=0

We get rid of parentheses

0.05Y^2-Y-1.5=0

We add all the numbers together, and all the variables

0.05Y^2-1Y-1.5=0

a = 0.05; b = -1; c = -1.5;
Δ = b2-4ac
Δ = -12-4·0.05·(-1.5)
Δ = 1.3
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{-(-1)-\sqrt{1.3}}{2*0.05}=\frac{1-\sqrt{1.3}}{0.1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.3}}{2*0.05}=\frac{1+\sqrt{1.3}}{0.1}
$