(2x+6)(2x+4)=52

Solution for (2x+6)(2x+4)=52 equation:

(2x+6)(2x+4)=52

We move all terms to the left:

(2x+6)(2x+4)-(52)=0

We multiply parentheses ..

(+4x^2+8x+12x+24)-52=0

We get rid of parentheses

4x^2+8x+12x+24-52=0

We add all the numbers together, and all the variables

4x^2+20x-28=0

a = 4; b = 20; c = -28;
Δ = b2-4ac
Δ = 202-4·4·(-28)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{53}}{2*4}=\frac{-20-4\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{53}}{2*4}=\frac{-20+4\sqrt{53}}{8}
$