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

Solution for 2(4w-1)(w-2)=0 equation:

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

We multiply parentheses ..

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

We multiply parentheses

8w^2-16w-2w+4=0

We add all the numbers together, and all the variables

8w^2-18w+4=0

a = 8; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·8·4
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14}{2*8}=\frac{4}{16}
=1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*8}=\frac{32}{16}
=2
$