4w^2-8w=w

Solution for 4w^2-8w=w equation:

4w^2-8w=w

We move all terms to the left:

4w^2-8w-(w)=0

We add all the numbers together, and all the variables

4w^2-9w=0

a = 4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·4·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*4}=\frac{0}{8}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*4}=\frac{18}{8}
=2+1/4
$