-3x(4x+1)=2x-1

Solution for -3x(4x+1)=2x-1 equation:

-3x(4x+1)=2x-1

We move all terms to the left:

-3x(4x+1)-(2x-1)=0

We multiply parentheses

-12x^2-3x-(2x-1)=0

We get rid of parentheses

-12x^2-3x-2x+1=0

We add all the numbers together, and all the variables

-12x^2-5x+1=0

a = -12; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-12)·1
Δ = 73
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{-(-5)-\sqrt{73}}{2*-12}=\frac{5-\sqrt{73}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-12}=\frac{5+\sqrt{73}}{-24}
$