-3(2x2-4)2+1=-11

Solution for -3(2x2-4)2+1=-11 equation:

-3(2x^2-4)2+1=-11

We move all terms to the left:

-3(2x^2-4)2+1-(-11)=0

We add all the numbers together, and all the variables

-3(2x^2-4)2+12=0

We multiply parentheses

-12x^2+24+12=0

We add all the numbers together, and all the variables

-12x^2+36=0

a = -12; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-12)·36
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-12}=\frac{0-24\sqrt{3}}{-24}
=-\frac{24\sqrt{3}}{-24}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-12}=\frac{0+24\sqrt{3}}{-24}
=\frac{24\sqrt{3}}{-24}
=\frac{\sqrt{3}}{-1}
$