(2x+8)(2x+12)=196

Solution for (2x+8)(2x+12)=196 equation:

(2x+8)(2x+12)=196

We move all terms to the left:

(2x+8)(2x+12)-(196)=0

We multiply parentheses ..

(+4x^2+24x+16x+96)-196=0

We get rid of parentheses

4x^2+24x+16x+96-196=0

We add all the numbers together, and all the variables

4x^2+40x-100=0

a = 4; b = 40; c = -100;
Δ = b2-4ac
Δ = 402-4·4·(-100)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{2}}{2*4}=\frac{-40-40\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{2}}{2*4}=\frac{-40+40\sqrt{2}}{8}
$