(x+12)(x)=72

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

(x+12)(x)=72

We move all terms to the left:

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

We multiply parentheses

x^2+12x-72=0

a = 1; b = 12; c = -72;
Δ = b2-4ac
Δ = 122-4·1·(-72)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{3}}{2*1}=\frac{-12-12\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{3}}{2*1}=\frac{-12+12\sqrt{3}}{2}
$