4(x-1)4x-1=19

Solution for 4(x-1)4x-1=19 equation:

4(x-1)4x-1=19

We move all terms to the left:

4(x-1)4x-1-(19)=0

We add all the numbers together, and all the variables

4(x-1)4x-20=0

We multiply parentheses

16x^2-16x-20=0

a = 16; b = -16; c = -20;
Δ = b2-4ac
Δ = -162-4·16·(-20)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{6}}{2*16}=\frac{16-16\sqrt{6}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{6}}{2*16}=\frac{16+16\sqrt{6}}{32}
$