(3x-24)(3x-5)=0

Solution for (3x-24)(3x-5)=0 equation:

(3x-24)(3x-5)=0

We multiply parentheses ..

(+9x^2-15x-72x+120)=0

We get rid of parentheses

9x^2-15x-72x+120=0

We add all the numbers together, and all the variables

9x^2-87x+120=0

a = 9; b = -87; c = +120;
Δ = b2-4ac
Δ = -872-4·9·120
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-57}{2*9}=\frac{30}{18}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+57}{2*9}=\frac{144}{18}
=8
$