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

Solution for 2(x^2-4x-32)=0 equation:

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

We multiply parentheses

2x^2-8x-64=0

a = 2; b = -8; c = -64;
Δ = b2-4ac
Δ = -82-4·2·(-64)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24}{2*2}=\frac{32}{4}
=8
$