(4x-1)(4x-1)-16x+4=0

Solution for (4x-1)(4x-1)-16x+4=0 equation:

(4x-1)(4x-1)-16x+4=0

We add all the numbers together, and all the variables

-16x+(4x-1)(4x-1)+4=0

We multiply parentheses ..

(+16x^2-4x-4x+1)-16x+4=0

We get rid of parentheses

16x^2-4x-4x-16x+1+4=0

We add all the numbers together, and all the variables

16x^2-24x+5=0

a = 16; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·16·5
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16}{2*16}=\frac{8}{32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16}{2*16}=\frac{40}{32}
=1+1/4
$