16(x-3)(2x-1)=1

Solution for 16(x-3)(2x-1)=1 equation:

16(x-3)(2x-1)=1

We move all terms to the left:

16(x-3)(2x-1)-(1)=0

We multiply parentheses ..

16(+2x^2-1x-6x+3)-1=0

We multiply parentheses

32x^2-16x-96x+48-1=0

We add all the numbers together, and all the variables

32x^2-112x+47=0

a = 32; b = -112; c = +47;
Δ = b2-4ac
Δ = -1122-4·32·47
Δ = 6528
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:

$\sqrt{\Delta}=\sqrt{6528}=\sqrt{64*102}=\sqrt{64}*\sqrt{102}=8\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-8\sqrt{102}}{2*32}=\frac{112-8\sqrt{102}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+8\sqrt{102}}{2*32}=\frac{112+8\sqrt{102}}{64}
$