w(w+4)=48

Solution for w(w+4)=48 equation:

w(w+4)=48

We move all terms to the left:

w(w+4)-(48)=0

We multiply parentheses

w^2+4w-48=0

a = 1; b = 4; c = -48;
Δ = b2-4ac
Δ = 42-4·1·(-48)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*1}=\frac{-4-4\sqrt{13}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*1}=\frac{-4+4\sqrt{13}}{2}
$