2x(x+24)=72

Solution for 2x(x+24)=72 equation:

2x(x+24)=72

We move all terms to the left:

2x(x+24)-(72)=0

We multiply parentheses

2x^2+48x-72=0

a = 2; b = 48; c = -72;
Δ = b2-4ac
Δ = 482-4·2·(-72)
Δ = 2880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{5}}{2*2}=\frac{-48-24\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{5}}{2*2}=\frac{-48+24\sqrt{5}}{4}
$