8s(s+3)=72

Solution for 8s(s+3)=72 equation:

8s(s+3)=72

We move all terms to the left:

8s(s+3)-(72)=0

We multiply parentheses

8s^2+24s-72=0

a = 8; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·8·(-72)
Δ = 2880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{5}}{2*8}=\frac{-24-24\sqrt{5}}{16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{5}}{2*8}=\frac{-24+24\sqrt{5}}{16}
$