(8+2w)(10+2w)=224

Solution for (8+2w)(10+2w)=224 equation:

(8+2w)(10+2w)=224

We move all terms to the left:

(8+2w)(10+2w)-(224)=0

We add all the numbers together, and all the variables

(2w+8)(2w+10)-224=0

We multiply parentheses ..

(+4w^2+20w+16w+80)-224=0

We get rid of parentheses

4w^2+20w+16w+80-224=0

We add all the numbers together, and all the variables

4w^2+36w-144=0

a = 4; b = 36; c = -144;
Δ = b2-4ac
Δ = 362-4·4·(-144)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-60}{2*4}=\frac{-96}{8}
=-12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+60}{2*4}=\frac{24}{8}
=3
$