3w(w-2)-16(w-2)=0

Solution for 3w(w-2)-16(w-2)=0 equation:

3w(w-2)-16(w-2)=0

We multiply parentheses

3w^2-6w-16w+32=0

We add all the numbers together, and all the variables

3w^2-22w+32=0

a = 3; b = -22; c = +32;
Δ = b2-4ac
Δ = -222-4·3·32
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{-(-22)-10}{2*3}=\frac{12}{6}
=2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10}{2*3}=\frac{32}{6}
=5+1/3
$