4(3x^2-64)=0

Solution for 4(3x^2-64)=0 equation:

4(3x^2-64)=0

We multiply parentheses

12x^2-256=0

a = 12; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·12·(-256)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*12}=\frac{0-64\sqrt{3}}{24}
=-\frac{64\sqrt{3}}{24}
=-\frac{8\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*12}=\frac{0+64\sqrt{3}}{24}
=\frac{64\sqrt{3}}{24}
=\frac{8\sqrt{3}}{3}
$