w(3w+4)=24

Solution for w(3w+4)=24 equation:

w(3w+4)=24

We move all terms to the left:

w(3w+4)-(24)=0

We multiply parentheses

3w^2+4w-24=0

a = 3; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·3·(-24)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{19}}{2*3}=\frac{-4-4\sqrt{19}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{19}}{2*3}=\frac{-4+4\sqrt{19}}{6}
$