31=-2x^2-16x

Solution for 31=-2x^2-16x equation:

31=-2x^2-16x

We move all terms to the left:

31-(-2x^2-16x)=0

We get rid of parentheses

2x^2+16x+31=0

a = 2; b = 16; c = +31;
Δ = b2-4ac
Δ = 162-4·2·31
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{2}}{2*2}=\frac{-16-2\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{2}}{2*2}=\frac{-16+2\sqrt{2}}{4}
$