8(3x^2-1)=0

Solution for 8(3x^2-1)=0 equation:

8(3x^2-1)=0

We multiply parentheses

24x^2-8=0

a = 24; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·24·(-8)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*24}=\frac{0-16\sqrt{3}}{48}
=-\frac{16\sqrt{3}}{48}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*24}=\frac{0+16\sqrt{3}}{48}
=\frac{16\sqrt{3}}{48}
=\frac{\sqrt{3}}{3}
$