6(w-8)2w=-24

Solution for 6(w-8)2w=-24 equation:

6(w-8)2w=-24

We move all terms to the left:

6(w-8)2w-(-24)=0

We add all the numbers together, and all the variables

6(w-8)2w+24=0

We multiply parentheses

12w^2-96w+24=0

a = 12; b = -96; c = +24;
Δ = b2-4ac
Δ = -962-4·12·24
Δ = 8064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-24\sqrt{14}}{2*12}=\frac{96-24\sqrt{14}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+24\sqrt{14}}{2*12}=\frac{96+24\sqrt{14}}{24}
$