(2x-1)(2x+1)=4x+1

Solution for (2x-1)(2x+1)=4x+1 equation:

(2x-1)(2x+1)=4x+1

We move all terms to the left:

(2x-1)(2x+1)-(4x+1)=0

We use the square of the difference formula

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

We get rid of parentheses

4x^2-4x-1-1=0

We add all the numbers together, and all the variables

4x^2-4x-2=0

a = 4; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·4·(-2)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*4}=\frac{4-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*4}=\frac{4+4\sqrt{3}}{8}
$