(2x+8)(2x+12)=100

Solution for (2x+8)(2x+12)=100 equation:

(2x+8)(2x+12)=100

We move all terms to the left:

(2x+8)(2x+12)-(100)=0

We multiply parentheses ..

(+4x^2+24x+16x+96)-100=0

We get rid of parentheses

4x^2+24x+16x+96-100=0

We add all the numbers together, and all the variables

4x^2+40x-4=0

a = 4; b = 40; c = -4;
Δ = b2-4ac
Δ = 402-4·4·(-4)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{26}}{2*4}=\frac{-40-8\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{26}}{2*4}=\frac{-40+8\sqrt{26}}{8}
$