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

Solution for (3x-1)(4x+2)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+2x-2=0

a = 12; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·12·(-2)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*12}=\frac{8}{24}
=1/3
$