((8+w)(4w+2))=0

Solution for ((8+w)(4w+2))=0 equation:

((8+w)(4w+2))=0

We add all the numbers together, and all the variables

((w+8)(4w+2))=0

We multiply parentheses ..

((+4w^2+2w+32w+16))=0


We calculate terms in parentheses: +((+4w^2+2w+32w+16)), so:

(+4w^2+2w+32w+16)

We get rid of parentheses

4w^2+2w+32w+16

We add all the numbers together, and all the variables

4w^2+34w+16

Back to the equation:

+(4w^2+34w+16)


We get rid of parentheses

4w^2+34w+16=0

a = 4; b = 34; c = +16;
Δ = b2-4ac
Δ = 342-4·4·16
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-30}{2*4}=\frac{-64}{8}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+30}{2*4}=\frac{-4}{8}
=-1/2
$