Y=-1.5x^2-6x

Solution for Y=-1.5x^2-6x equation:

=-1.5Y^2-6Y

We move all terms to the left:

-(-1.5Y^2-6Y)=0

We get rid of parentheses

1.5Y^2+6Y=0

a = 1.5; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·1.5·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*1.5}=\frac{-12}{3}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*1.5}=\frac{0}{3}
=0
$