Y=-2x^2-9x-5

Solution for Y=-2x^2-9x-5 equation:

=-2Y^2-9Y-5

We move all terms to the left:

-(-2Y^2-9Y-5)=0

We get rid of parentheses

2Y^2+9Y+5=0

a = 2; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·2·5
Δ = 41
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{-(9)-\sqrt{41}}{2*2}=\frac{-9-\sqrt{41}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*2}=\frac{-9+\sqrt{41}}{4}
$