(2x+1)(6x-4)=0

Solution for (2x+1)(6x-4)=0 equation:

(2x+1)(6x-4)=0

We multiply parentheses ..

(+12x^2-8x+6x-4)=0

We get rid of parentheses

12x^2-8x+6x-4=0

We add all the numbers together, and all the variables

12x^2-2x-4=0

a = 12; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·12·(-4)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*12}=\frac{16}{24}
=2/3
$