(8x+2)(3x-9)=0

Solution for (8x+2)(3x-9)=0 equation:

(8x+2)(3x-9)=0

We multiply parentheses ..

(+24x^2-72x+6x-18)=0

We get rid of parentheses

24x^2-72x+6x-18=0

We add all the numbers together, and all the variables

24x^2-66x-18=0

a = 24; b = -66; c = -18;
Δ = b2-4ac
Δ = -662-4·24·(-18)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-78}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+78}{2*24}=\frac{144}{48}
=3
$