8w=2w^2-16w

Solution for 8w=2w^2-16w equation:

8w=2w^2-16w

We move all terms to the left:

8w-(2w^2-16w)=0

We get rid of parentheses

-2w^2+8w+16w=0

We add all the numbers together, and all the variables

-2w^2+24w=0

a = -2; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-2)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-2}=\frac{-48}{-4}
=+12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-2}=\frac{0}{-4}
=0
$