(-3x+7)(2x-4)=0

Solution for (-3x+7)(2x-4)=0 equation:

(-3x+7)(2x-4)=0

We multiply parentheses ..

(-6x^2+12x+14x-28)=0

We get rid of parentheses

-6x^2+12x+14x-28=0

We add all the numbers together, and all the variables

-6x^2+26x-28=0

a = -6; b = 26; c = -28;
Δ = b2-4ac
Δ = 262-4·(-6)·(-28)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2}{2*-6}=\frac{-24}{-12}
=+2
$