2(3w-5)2w=782

Solution for 2(3w-5)2w=782 equation:

2(3w-5)2w=782

We move all terms to the left:

2(3w-5)2w-(782)=0

We multiply parentheses

12w^2-20w-782=0

a = 12; b = -20; c = -782;
Δ = b2-4ac
Δ = -202-4·12·(-782)
Δ = 37936
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:

$\sqrt{\Delta}=\sqrt{37936}=\sqrt{16*2371}=\sqrt{16}*\sqrt{2371}=4\sqrt{2371}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{2371}}{2*12}=\frac{20-4\sqrt{2371}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{2371}}{2*12}=\frac{20+4\sqrt{2371}}{24}
$