12=(w+1)(w)

Solution for 12=(w+1)(w) equation:

12=(w+1)(w)

We move all terms to the left:

12-((w+1)(w))=0


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

(w+1)w

We multiply parentheses

w^2+w

Back to the equation:

-(w^2+w)


We get rid of parentheses

-w^2-w+12=0

We add all the numbers together, and all the variables

-1w^2-1w+12=0

a = -1; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-1)·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-1}=\frac{-6}{-2}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-1}=\frac{8}{-2}
=-4
$