128=68w-2w^2

Solution for 128=68w-2w^2 equation:

128=68w-2w^2

We move all terms to the left:

128-(68w-2w^2)=0

We get rid of parentheses

2w^2-68w+128=0

a = 2; b = -68; c = +128;
Δ = b2-4ac
Δ = -682-4·2·128
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-60}{2*2}=\frac{8}{4}
=2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+60}{2*2}=\frac{128}{4}
=32
$