220=(w+4)(2w+6)

Solution for 220=(w+4)(2w+6) equation:

220=(w+4)(2w+6)

We move all terms to the left:

220-((w+4)(2w+6))=0

We multiply parentheses ..

-((+2w^2+6w+8w+24))+220=0


We calculate terms in parentheses: -((+2w^2+6w+8w+24)), so:

(+2w^2+6w+8w+24)

We get rid of parentheses

2w^2+6w+8w+24

We add all the numbers together, and all the variables

2w^2+14w+24

Back to the equation:

-(2w^2+14w+24)


We get rid of parentheses

-2w^2-14w-24+220=0

We add all the numbers together, and all the variables

-2w^2-14w+196=0

a = -2; b = -14; c = +196;
Δ = b2-4ac
Δ = -142-4·(-2)·196
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-42}{2*-2}=\frac{-28}{-4}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+42}{2*-2}=\frac{56}{-4}
=-14
$