(4x+3)(4x-3)=x

Solution for (4x+3)(4x-3)=x equation:

(4x+3)(4x-3)=x

We move all terms to the left:

(4x+3)(4x-3)-(x)=0

We add all the numbers together, and all the variables

-1x+(4x+3)(4x-3)=0

We use the square of the difference formula

16x^2-1x-9=0

a = 16; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·16·(-9)
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{577}}{2*16}=\frac{1-\sqrt{577}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{577}}{2*16}=\frac{1+\sqrt{577}}{32}
$