(x+4)(x-8)=32

Solution for (x+4)(x-8)=32 equation:

(x+4)(x-8)=32

We move all terms to the left:

(x+4)(x-8)-(32)=0

We multiply parentheses ..

(+x^2-8x+4x-32)-32=0

We get rid of parentheses

x^2-8x+4x-32-32=0

We add all the numbers together, and all the variables

x^2-4x-64=0

a = 1; b = -4; c = -64;
Δ = b2-4ac
Δ = -42-4·1·(-64)
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{-(-4)-4\sqrt{17}}{2*1}=\frac{4-4\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{17}}{2*1}=\frac{4+4\sqrt{17}}{2}
$