(-2x-1)(6x-1)=0

Solution for (-2x-1)(6x-1)=0 equation:

(-2x-1)(6x-1)=0

We multiply parentheses ..

(-12x^2+2x-6x+1)=0

We get rid of parentheses

-12x^2+2x-6x+1=0

We add all the numbers together, and all the variables

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

a = -12; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-12)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-12}=\frac{-4}{-24}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-12}=\frac{12}{-24}
=-1/2
$