(4+2x)(6+2x)-24=24

Solution for (4+2x)(6+2x)-24=24 equation:

(4+2x)(6+2x)-24=24

We move all terms to the left:

(4+2x)(6+2x)-24-(24)=0

We add all the numbers together, and all the variables

(2x+4)(2x+6)-24-24=0

We add all the numbers together, and all the variables

(2x+4)(2x+6)-48=0

We multiply parentheses ..

(+4x^2+12x+8x+24)-48=0

We get rid of parentheses

4x^2+12x+8x+24-48=0

We add all the numbers together, and all the variables

4x^2+20x-24=0

a = 4; b = 20; c = -24;
Δ = b2-4ac
Δ = 202-4·4·(-24)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-28}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*4}=\frac{8}{8}
=1
$