w(3+w)=30

Solution for w(3+w)=30 equation:

w(3+w)=30

We move all terms to the left:

w(3+w)-(30)=0

We add all the numbers together, and all the variables

w(w+3)-30=0

We multiply parentheses

w^2+3w-30=0

a = 1; b = 3; c = -30;
Δ = b2-4ac
Δ = 32-4·1·(-30)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{129}}{2*1}=\frac{-3-\sqrt{129}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*1}=\frac{-3+\sqrt{129}}{2}
$