3(x-4)9=-6(x2)-9

Solution for 3(x-4)9=-6(x2)-9 equation:

3(x-4)9=-6(x2)-9

We move all terms to the left:

3(x-4)9-(-6(x2)-9)=0

We add all the numbers together, and all the variables

-(-6x^2-9)+3(x-4)9=0

We multiply parentheses

-(-6x^2-9)+27x-108=0

We get rid of parentheses

6x^2+27x+9-108=0

We add all the numbers together, and all the variables

6x^2+27x-99=0

a = 6; b = 27; c = -99;
Δ = b2-4ac
Δ = 272-4·6·(-99)
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{345}}{2*6}=\frac{-27-3\sqrt{345}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{345}}{2*6}=\frac{-27+3\sqrt{345}}{12}
$