(6+2x)(8+2x)=48

Solution for (6+2x)(8+2x)=48 equation:

(6+2x)(8+2x)=48

We move all terms to the left:

(6+2x)(8+2x)-(48)=0

We add all the numbers together, and all the variables

(2x+6)(2x+8)-48=0

We multiply parentheses ..

(+4x^2+16x+12x+48)-48=0

We get rid of parentheses

4x^2+16x+12x+48-48=0

We add all the numbers together, and all the variables

4x^2+28x=0

a = 4; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·4·0
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{-(28)-28}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*4}=\frac{0}{8}
=0
$