(x+16)(x+32)=924

Solution for (x+16)(x+32)=924 equation:

(x+16)(x+32)=924

We move all terms to the left:

(x+16)(x+32)-(924)=0

We multiply parentheses ..

(+x^2+32x+16x+512)-924=0

We get rid of parentheses

x^2+32x+16x+512-924=0

We add all the numbers together, and all the variables

x^2+48x-412=0

a = 1; b = 48; c = -412;
Δ = b2-4ac
Δ = 482-4·1·(-412)
Δ = 3952
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:

$\sqrt{\Delta}=\sqrt{3952}=\sqrt{16*247}=\sqrt{16}*\sqrt{247}=4\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{247}}{2*1}=\frac{-48-4\sqrt{247}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{247}}{2*1}=\frac{-48+4\sqrt{247}}{2}
$