(8+w)(4w+3)=w

Solution for (8+w)(4w+3)=w equation:

(8+w)(4w+3)=w

We move all terms to the left:

(8+w)(4w+3)-(w)=0

We add all the numbers together, and all the variables

(w+8)(4w+3)-w=0

We add all the numbers together, and all the variables

-1w+(w+8)(4w+3)=0

We multiply parentheses ..

(+4w^2+3w+32w+24)-1w=0

We get rid of parentheses

4w^2+3w+32w-1w+24=0

We add all the numbers together, and all the variables

4w^2+34w+24=0

a = 4; b = 34; c = +24;
Δ = b2-4ac
Δ = 342-4·4·24
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{193}}{2*4}=\frac{-34-2\sqrt{193}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{193}}{2*4}=\frac{-34+2\sqrt{193}}{8}
$