(2w+8)(2w+8)+w+w=34

Solution for (2w+8)(2w+8)+w+w=34 equation:

(2w+8)(2w+8)+w+w=34

We move all terms to the left:

(2w+8)(2w+8)+w+w-(34)=0

We add all the numbers together, and all the variables

2w+(2w+8)(2w+8)-34=0

We multiply parentheses ..

(+4w^2+16w+16w+64)+2w-34=0

We get rid of parentheses

4w^2+16w+16w+2w+64-34=0

We add all the numbers together, and all the variables

4w^2+34w+30=0

a = 4; b = 34; c = +30;
Δ = b2-4ac
Δ = 342-4·4·30
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-26}{2*4}=\frac{-60}{8}
=-7+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+26}{2*4}=\frac{-8}{8}
=-1
$