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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

a = -24; b = 72; c = +6;
Δ = b2-4ac
Δ = 722-4·(-24)·6
Δ = 5760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{10}}{2*-24}=\frac{-72-24\sqrt{10}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{10}}{2*-24}=\frac{-72+24\sqrt{10}}{-48}
$