x(4x-1)=12x-1

Solution for x(4x-1)=12x-1 equation:

x(4x-1)=12x-1

We move all terms to the left:

x(4x-1)-(12x-1)=0

We multiply parentheses

4x^2-1x-(12x-1)=0

We get rid of parentheses

4x^2-1x-12x+1=0

We add all the numbers together, and all the variables

4x^2-13x+1=0

a = 4; b = -13; c = +1;
Δ = b2-4ac
Δ = -132-4·4·1
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{17}}{2*4}=\frac{13-3\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{17}}{2*4}=\frac{13+3\sqrt{17}}{8}
$