2(2w^2-8w+7)=0

Solution for 2(2w^2-8w+7)=0 equation:

2(2w^2-8w+7)=0

We multiply parentheses

4w^2-16w+14=0

a = 4; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·4·14
Δ = 32
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:

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