(3x-27)(-8x+12)=0

Solution for (3x-27)(-8x+12)=0 equation:

(3x-27)(-8x+12)=0

We multiply parentheses ..

(-24x^2+36x+216x-324)=0

We get rid of parentheses

-24x^2+36x+216x-324=0

We add all the numbers together, and all the variables

-24x^2+252x-324=0

a = -24; b = 252; c = -324;
Δ = b2-4ac
Δ = 2522-4·(-24)·(-324)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-180}{2*-24}=\frac{-432}{-48}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+180}{2*-24}=\frac{-72}{-48}
=1+1/2
$