(3x-6)(3-4x)=0

Solution for (3x-6)(3-4x)=0 equation:

(3x-6)(3-4x)=0

We add all the numbers together, and all the variables

(3x-6)(-4x+3)=0

We multiply parentheses ..

(-12x^2+9x+24x-18)=0

We get rid of parentheses

-12x^2+9x+24x-18=0

We add all the numbers together, and all the variables

-12x^2+33x-18=0

a = -12; b = 33; c = -18;
Δ = b2-4ac
Δ = 332-4·(-12)·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-15}{2*-12}=\frac{-48}{-24}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+15}{2*-12}=\frac{-18}{-24}
=3/4
$