2w(w+18)=58

Solution for 2w(w+18)=58 equation:

2w(w+18)=58

We move all terms to the left:

2w(w+18)-(58)=0

We multiply parentheses

2w^2+36w-58=0

a = 2; b = 36; c = -58;
Δ = b2-4ac
Δ = 362-4·2·(-58)
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{110}}{2*2}=\frac{-36-4\sqrt{110}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{110}}{2*2}=\frac{-36+4\sqrt{110}}{4}
$