12x(x+12)=72

Solution for 12x(x+12)=72 equation:

12x(x+12)=72

We move all terms to the left:

12x(x+12)-(72)=0

We multiply parentheses

12x^2+144x-72=0

a = 12; b = 144; c = -72;
Δ = b2-4ac
Δ = 1442-4·12·(-72)
Δ = 24192
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:

$\sqrt{\Delta}=\sqrt{24192}=\sqrt{576*42}=\sqrt{576}*\sqrt{42}=24\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-24\sqrt{42}}{2*12}=\frac{-144-24\sqrt{42}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+24\sqrt{42}}{2*12}=\frac{-144+24\sqrt{42}}{24}
$