4x(2x+3)=-2

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

4x(2x+3)=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+12x+2=0

a = 8; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·8·2
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*8}=\frac{-12-4\sqrt{5}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*8}=\frac{-12+4\sqrt{5}}{16}
$