12+4x(2x+4)=68

Solution for 12+4x(2x+4)=68 equation:

12+4x(2x+4)=68

We move all terms to the left:

12+4x(2x+4)-(68)=0

We add all the numbers together, and all the variables

4x(2x+4)-56=0

We multiply parentheses

8x^2+16x-56=0

a = 8; b = 16; c = -56;
Δ = b2-4ac
Δ = 162-4·8·(-56)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32\sqrt{2}}{2*8}=\frac{-16-32\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32\sqrt{2}}{2*8}=\frac{-16+32\sqrt{2}}{16}
$