4x(2x+3)=-2x-4

Solution for 4x(2x+3)=-2x-4 equation:

4x(2x+3)=-2x-4

We move all terms to the left:

4x(2x+3)-(-2x-4)=0

We multiply parentheses

8x^2+12x-(-2x-4)=0

We get rid of parentheses

8x^2+12x+2x+4=0

We add all the numbers together, and all the variables

8x^2+14x+4=0

a = 8; b = 14; c = +4;
Δ = b2-4ac
Δ = 142-4·8·4
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{17}}{2*8}=\frac{-14-2\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{17}}{2*8}=\frac{-14+2\sqrt{17}}{16}
$