(3x-9)(-4x+16)=0

Solution for (3x-9)(-4x+16)=0 equation:

(3x-9)(-4x+16)=0

We multiply parentheses ..

(-12x^2+48x+36x-144)=0

We get rid of parentheses

-12x^2+48x+36x-144=0

We add all the numbers together, and all the variables

-12x^2+84x-144=0

a = -12; b = 84; c = -144;
Δ = b2-4ac
Δ = 842-4·(-12)·(-144)
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{-(84)-12}{2*-12}=\frac{-96}{-24}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12}{2*-12}=\frac{-72}{-24}
=+3
$