2(4+w)w=42

Solution for 2(4+w)w=42 equation:

2(4+w)w=42

We move all terms to the left:

2(4+w)w-(42)=0

We add all the numbers together, and all the variables

2(w+4)w-42=0

We multiply parentheses

2w^2+8w-42=0

a = 2; b = 8; c = -42;
Δ = b2-4ac
Δ = 82-4·2·(-42)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-20}{2*2}=\frac{-28}{4}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+20}{2*2}=\frac{12}{4}
=3
$