Y=-2x^2-16x-20

Solution for Y=-2x^2-16x-20 equation:

=-2Y^2-16Y-20

We move all terms to the left:

-(-2Y^2-16Y-20)=0

We get rid of parentheses

2Y^2+16Y+20=0

a = 2; b = 16; c = +20;
Δ = b2-4ac
Δ = 162-4·2·20
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{6}}{2*2}=\frac{-16-4\sqrt{6}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{6}}{2*2}=\frac{-16+4\sqrt{6}}{4}
$