2(3w-8)(2w)=40

Solution for 2(3w-8)(2w)=40 equation:

2(3w-8)(2w)=40

We move all terms to the left:

2(3w-8)(2w)-(40)=0

We multiply parentheses

12w^2-32w-40=0

a = 12; b = -32; c = -40;
Δ = b2-4ac
Δ = -322-4·12·(-40)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{46}}{2*12}=\frac{32-8\sqrt{46}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{46}}{2*12}=\frac{32+8\sqrt{46}}{24}
$