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

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

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

We move all terms to the left:

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

We multiply parentheses

8w^2+12w-(-2w-3)=0

We get rid of parentheses

8w^2+12w+2w+3=0

We add all the numbers together, and all the variables

8w^2+14w+3=0

a = 8; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·8·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*8}=\frac{-24}{16}
=-1+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*8}=\frac{-4}{16}
=-1/4
$