(6x-9)(2x+8)=0

Solution for (6x-9)(2x+8)=0 equation:

(6x-9)(2x+8)=0

We multiply parentheses ..

(+12x^2+48x-18x-72)=0

We get rid of parentheses

12x^2+48x-18x-72=0

We add all the numbers together, and all the variables

12x^2+30x-72=0

a = 12; b = 30; c = -72;
Δ = b2-4ac
Δ = 302-4·12·(-72)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-66}{2*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+66}{2*12}=\frac{36}{24}
=1+1/2
$