(6x-9)(3x+8)=0

Solution for (6x-9)(3x+8)=0 equation:

(6x-9)(3x+8)=0

We multiply parentheses ..

(+18x^2+48x-27x-72)=0

We get rid of parentheses

18x^2+48x-27x-72=0

We add all the numbers together, and all the variables

18x^2+21x-72=0

a = 18; b = 21; c = -72;
Δ = b2-4ac
Δ = 212-4·18·(-72)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-75}{2*18}=\frac{-96}{36}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+75}{2*18}=\frac{54}{36}
=1+1/2
$