66=(2w+1)(w)

Solution for 66=(2w+1)(w) equation:

66=(2w+1)(w)

We move all terms to the left:

66-((2w+1)(w))=0


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

(2w+1)w

We multiply parentheses

2w^2+w

Back to the equation:

-(2w^2+w)


We get rid of parentheses

-2w^2-w+66=0

We add all the numbers together, and all the variables

-2w^2-1w+66=0

a = -2; b = -1; c = +66;
Δ = b2-4ac
Δ = -12-4·(-2)·66
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*-2}=\frac{24}{-4}
=-6
$