2w(4w+1)=4w+1

Solution for 2w(4w+1)=4w+1 equation:

2w(4w+1)=4w+1

We move all terms to the left:

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

We multiply parentheses

8w^2+2w-(4w+1)=0

We get rid of parentheses

8w^2+2w-4w-1=0

We add all the numbers together, and all the variables

8w^2-2w-1=0

a = 8; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·8·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*8}=\frac{-4}{16}
=-1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*8}=\frac{8}{16}
=1/2
$