Y=-0.5x^2-3x+1

Solution for Y=-0.5x^2-3x+1 equation:

=-0.5Y^2-3Y+1

We move all terms to the left:

-(-0.5Y^2-3Y+1)=0

We get rid of parentheses

0.5Y^2+3Y-1=0

a = 0.5; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·0.5·(-1)
Δ = 11
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{-(3)-\sqrt{11}}{2*0.5}=\frac{-3-\sqrt{11}}{1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{11}}{2*0.5}=\frac{-3+\sqrt{11}}{1}
$