(2+x)(4+x)=32

Solution for (2+x)(4+x)=32 equation:

(2+x)(4+x)=32

We move all terms to the left:

(2+x)(4+x)-(32)=0

We add all the numbers together, and all the variables

(x+2)(x+4)-32=0

We multiply parentheses ..

(+x^2+4x+2x+8)-32=0

We get rid of parentheses

x^2+4x+2x+8-32=0

We add all the numbers together, and all the variables

x^2+6x-24=0

a = 1; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·1·(-24)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*1}=\frac{-6-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*1}=\frac{-6+2\sqrt{33}}{2}
$