0=64-12x^2

Solution for 0=64-12x^2 equation:

0=64-12x^2

We move all terms to the left:

0-(64-12x^2)=0

We add all the numbers together, and all the variables

-(64-12x^2)=0

We get rid of parentheses

12x^2-64=0

a = 12; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·12·(-64)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*12}=\frac{0-32\sqrt{3}}{24}
=-\frac{32\sqrt{3}}{24}
=-\frac{4\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*12}=\frac{0+32\sqrt{3}}{24}
=\frac{32\sqrt{3}}{24}
=\frac{4\sqrt{3}}{3}
$