(x+12)(x+16)=288

Solution for (x+12)(x+16)=288 equation:

(x+12)(x+16)=288

We move all terms to the left:

(x+12)(x+16)-(288)=0

We multiply parentheses ..

(+x^2+16x+12x+192)-288=0

We get rid of parentheses

x^2+16x+12x+192-288=0

We add all the numbers together, and all the variables

x^2+28x-96=0

a = 1; b = 28; c = -96;
Δ = b2-4ac
Δ = 282-4·1·(-96)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{73}}{2*1}=\frac{-28-4\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{73}}{2*1}=\frac{-28+4\sqrt{73}}{2}
$