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

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

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

We multiply parentheses ..

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

We get rid of parentheses

12x^2-6x+2x-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
$