Y=-2x^2-8x-1

Solution for Y=-2x^2-8x-1 equation:

=-2Y^2-8Y-1

We move all terms to the left:

-(-2Y^2-8Y-1)=0

We get rid of parentheses

2Y^2+8Y+1=0

a = 2; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*2}=\frac{-8-2\sqrt{14}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*2}=\frac{-8+2\sqrt{14}}{4}
$