(-3x+6)(8x-20)=0

Solution for (-3x+6)(8x-20)=0 equation:

(-3x+6)(8x-20)=0

We multiply parentheses ..

(-24x^2+60x+48x-120)=0

We get rid of parentheses

-24x^2+60x+48x-120=0

We add all the numbers together, and all the variables

-24x^2+108x-120=0

a = -24; b = 108; c = -120;
Δ = b2-4ac
Δ = 1082-4·(-24)·(-120)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12}{2*-24}=\frac{-120}{-48}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12}{2*-24}=\frac{-96}{-48}
=+2
$