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

Solution for 4((3)^2x-3)=11 equation:

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

We move all terms to the left:

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

We multiply parentheses

12x^2-12-11=0

We add all the numbers together, and all the variables

12x^2-23=0

a = 12; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·12·(-23)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{69}}{2*12}=\frac{0-4\sqrt{69}}{24}
=-\frac{4\sqrt{69}}{24}
=-\frac{\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{69}}{2*12}=\frac{0+4\sqrt{69}}{24}
=\frac{4\sqrt{69}}{24}
=\frac{\sqrt{69}}{6}
$