(x+2)(x+6)=64

Solution for (x+2)(x+6)=64 equation:

(x+2)(x+6)=64

We move all terms to the left:

(x+2)(x+6)-(64)=0

We multiply parentheses ..

(+x^2+6x+2x+12)-64=0

We get rid of parentheses

x^2+6x+2x+12-64=0

We add all the numbers together, and all the variables

x^2+8x-52=0

a = 1; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·1·(-52)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{17}}{2*1}=\frac{-8-4\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{17}}{2*1}=\frac{-8+4\sqrt{17}}{2}
$