0=4-12x^2-4x

Solution for 0=4-12x^2-4x equation:

0=4-12x^2-4x

We move all terms to the left:

0-(4-12x^2-4x)=0

We add all the numbers together, and all the variables

-(4-12x^2-4x)=0

We get rid of parentheses

12x^2+4x-4=0

a = 12; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·12·(-4)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*12}=\frac{-4-4\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*12}=\frac{-4+4\sqrt{13}}{24}
$