21=(2w-1)(w)

Solution for 21=(2w-1)(w) equation:

21=(2w-1)(w)

We move all terms to the left:

21-((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+21=0

We add all the numbers together, and all the variables

-2w^2+w+21=0

a = -2; b = 1; c = +21;
Δ = b2-4ac
Δ = 12-4·(-2)·21
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*-2}=\frac{12}{-4}
=-3
$