28=(2w-1)w

Solution for 28=(2w-1)w equation:

28=(2w-1)w

We move all terms to the left:

28-((2w-1)w)=0


We calculate terms in parentheses: -((2w-1)w), so:

(2w-1)w

We multiply parentheses

2w^2-1w

Back to the equation:

-(2w^2-1w)


We get rid of parentheses

-2w^2+1w+28=0

We add all the numbers together, and all the variables

-2w^2+w+28=0

a = -2; b = 1; c = +28;
Δ = b2-4ac
Δ = 12-4·(-2)·28
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-2}=\frac{-16}{-4}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-2}=\frac{14}{-4}
=-3+1/2
$