(2w+4)w=86

Solution for (2w+4)w=86 equation:

(2w+4)w=86

We move all terms to the left:

(2w+4)w-(86)=0

We multiply parentheses

2w^2+4w-86=0

a = 2; b = 4; c = -86;
Δ = b2-4ac
Δ = 42-4·2·(-86)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{11}}{2*2}=\frac{-4-8\sqrt{11}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{11}}{2*2}=\frac{-4+8\sqrt{11}}{4}
$