3(4x^2-4)-8=0

Solution for 3(4x^2-4)-8=0 equation:

3(4x^2-4)-8=0

We multiply parentheses

12x^2-12-8=0

We add all the numbers together, and all the variables

12x^2-20=0

a = 12; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·12·(-20)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*12}=\frac{0-8\sqrt{15}}{24}
=-\frac{8\sqrt{15}}{24}
=-\frac{\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*12}=\frac{0+8\sqrt{15}}{24}
=\frac{8\sqrt{15}}{24}
=\frac{\sqrt{15}}{3}
$