0=-2x^2-16x-27

Solution for 0=-2x^2-16x-27 equation:

0=-2x^2-16x-27

We move all terms to the left:

0-(-2x^2-16x-27)=0

We add all the numbers together, and all the variables

-(-2x^2-16x-27)=0

We get rid of parentheses

2x^2+16x+27=0

a = 2; b = 16; c = +27;
Δ = b2-4ac
Δ = 162-4·2·27
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{10}}{2*2}=\frac{-16-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{10}}{2*2}=\frac{-16+2\sqrt{10}}{4}
$