68=(2x+6)(2x+2)

Solution for 68=(2x+6)(2x+2) equation:

68=(2x+6)(2x+2)

We move all terms to the left:

68-((2x+6)(2x+2))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((+4x^2+4x+12x+12)), so:

(+4x^2+4x+12x+12)

We get rid of parentheses

4x^2+4x+12x+12

We add all the numbers together, and all the variables

4x^2+16x+12

Back to the equation:

-(4x^2+16x+12)


We get rid of parentheses

-4x^2-16x-12+68=0

We add all the numbers together, and all the variables

-4x^2-16x+56=0

a = -4; b = -16; c = +56;
Δ = b2-4ac
Δ = -162-4·(-4)·56
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-24\sqrt{2}}{2*-4}=\frac{16-24\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+24\sqrt{2}}{2*-4}=\frac{16+24\sqrt{2}}{-8}
$