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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+14x-4=0

a = -6; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·(-6)·(-4)
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{-(14)-10}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-6}=\frac{-4}{-12}
=1/3
$