6x(2x+4)+2x+4=96

Solution for 6x(2x+4)+2x+4=96 equation:

6x(2x+4)+2x+4=96

We move all terms to the left:

6x(2x+4)+2x+4-(96)=0

We add all the numbers together, and all the variables

2x+6x(2x+4)-92=0

We multiply parentheses

12x^2+2x+24x-92=0

We add all the numbers together, and all the variables

12x^2+26x-92=0

a = 12; b = 26; c = -92;
Δ = b2-4ac
Δ = 262-4·12·(-92)
Δ = 5092
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:

$\sqrt{\Delta}=\sqrt{5092}=\sqrt{4*1273}=\sqrt{4}*\sqrt{1273}=2\sqrt{1273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1273}}{2*12}=\frac{-26-2\sqrt{1273}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1273}}{2*12}=\frac{-26+2\sqrt{1273}}{24}
$