(9x-18)(24-6x)=0

Solution for (9x-18)(24-6x)=0 equation:

(9x-18)(24-6x)=0

We add all the numbers together, and all the variables

(9x-18)(-6x+24)=0

We multiply parentheses ..

(-54x^2+216x+108x-432)=0

We get rid of parentheses

-54x^2+216x+108x-432=0

We add all the numbers together, and all the variables

-54x^2+324x-432=0

a = -54; b = 324; c = -432;
Δ = b2-4ac
Δ = 3242-4·(-54)·(-432)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-108}{2*-54}=\frac{-432}{-108}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+108}{2*-54}=\frac{-216}{-108}
=+2
$