(3x-4)(3x+4)-9(x-1)2-11=0

Solution for (3x-4)(3x+4)-9(x-1)2-11=0 equation:

(3x-4)(3x+4)-9(x-1)2-11=0

We use the square of the difference formula

9x^2-9(x-1)2-16-11=0

We multiply parentheses

9x^2-18x+18-16-11=0

We add all the numbers together, and all the variables

9x^2-18x-9=0

a = 9; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·9·(-9)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{2}}{2*9}=\frac{18-18\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{2}}{2*9}=\frac{18+18\sqrt{2}}{18}
$