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

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

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

We multiply parentheses ..

(+24x^2+27x-48x-54)=0

We get rid of parentheses

24x^2+27x-48x-54=0

We add all the numbers together, and all the variables

24x^2-21x-54=0

a = 24; b = -21; c = -54;
Δ = b2-4ac
Δ = -212-4·24·(-54)
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*24}=\frac{-54}{48}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+75}{2*24}=\frac{96}{48}
=2
$