3x(4x-4)=-1

Solution for 3x(4x-4)=-1 equation:

3x(4x-4)=-1

We move all terms to the left:

3x(4x-4)-(-1)=0

We add all the numbers together, and all the variables

3x(4x-4)+1=0

We multiply parentheses

12x^2-12x+1=0

a = 12; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·12·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*12}=\frac{12-4\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*12}=\frac{12+4\sqrt{6}}{24}
$