(6+2x)(8+2x)=100

Solution for (6+2x)(8+2x)=100 equation:

(6+2x)(8+2x)=100

We move all terms to the left:

(6+2x)(8+2x)-(100)=0

We add all the numbers together, and all the variables

(2x+6)(2x+8)-100=0

We multiply parentheses ..

(+4x^2+16x+12x+48)-100=0

We get rid of parentheses

4x^2+16x+12x+48-100=0

We add all the numbers together, and all the variables

4x^2+28x-52=0

a = 4; b = 28; c = -52;
Δ = b2-4ac
Δ = 282-4·4·(-52)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{101}}{2*4}=\frac{-28-4\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{101}}{2*4}=\frac{-28+4\sqrt{101}}{8}
$