(W+8)(w+8)(w+8)=51

Solution for (W+8)(w+8)(w+8)=51 equation:

(+8)(W+8)(W+8)=51

We move all terms to the left:

(+8)(W+8)(W+8)-(51)=0

We add all the numbers together, and all the variables

8(W+8)(W+8)-51=0

We multiply parentheses ..

8(+W^2+8W+8W+64)-51=0

We multiply parentheses

8W^2+64W+64W+512-51=0

We add all the numbers together, and all the variables

8W^2+128W+461=0

a = 8; b = 128; c = +461;
Δ = b2-4ac
Δ = 1282-4·8·461
Δ = 1632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-4\sqrt{102}}{2*8}=\frac{-128-4\sqrt{102}}{16}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+4\sqrt{102}}{2*8}=\frac{-128+4\sqrt{102}}{16}
$