(6x+1)(6x-1)=1

Solution for (6x+1)(6x-1)=1 equation:

(6x+1)(6x-1)=1

We move all terms to the left:

(6x+1)(6x-1)-(1)=0

We use the square of the difference formula

36x^2-1-1=0

We add all the numbers together, and all the variables

36x^2-2=0

a = 36; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·36·(-2)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*36}=\frac{0-12\sqrt{2}}{72}
=-\frac{12\sqrt{2}}{72}
=-\frac{\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*36}=\frac{0+12\sqrt{2}}{72}
=\frac{12\sqrt{2}}{72}
=\frac{\sqrt{2}}{6}
$