32(x^2-8)=0

Solution for 32(x^2-8)=0 equation:

32(x^2-8)=0

We multiply parentheses

32x^2-256=0

a = 32; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·32·(-256)
Δ = 32768
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:

$\sqrt{\Delta}=\sqrt{32768}=\sqrt{16384*2}=\sqrt{16384}*\sqrt{2}=128\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{2}}{2*32}=\frac{0-128\sqrt{2}}{64}
=-\frac{128\sqrt{2}}{64}
=-2\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{2}}{2*32}=\frac{0+128\sqrt{2}}{64}
=\frac{128\sqrt{2}}{64}
=2\sqrt{2}
$