8(n+2)(n+4)=1,144.

Solution for 8(n+2)(n+4)=1,144. equation:

8(n+2)(n+4)=1.144.

We move all terms to the left:

8(n+2)(n+4)-(1.144.)=0

We add all the numbers together, and all the variables

8(n+2)(n+4)-0=0

We add all the numbers together, and all the variables

8(n+2)(n+4)=0

We multiply parentheses ..

8(+n^2+4n+2n+8)=0

We multiply parentheses

8n^2+32n+16n+64=0

We add all the numbers together, and all the variables

8n^2+48n+64=0

a = 8; b = 48; c = +64;
Δ = b2-4ac
Δ = 482-4·8·64
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16}{2*8}=\frac{-64}{16}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16}{2*8}=\frac{-32}{16}
=-2
$