2x(x+4)+1=-1

Solution for 2x(x+4)+1=-1 equation:

2x(x+4)+1=-1

We move all terms to the left:

2x(x+4)+1-(-1)=0

We add all the numbers together, and all the variables

2x(x+4)+2=0

We multiply parentheses

2x^2+8x+2=0

a = 2; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·2·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3}}{2*2}=\frac{-8-4\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3}}{2*2}=\frac{-8+4\sqrt{3}}{4}
$