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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -(3(4x+6)x), so:

3(4x+6)x

We multiply parentheses

12x^2+18x

Back to the equation:

-(12x^2+18x)


We add all the numbers together, and all the variables

-9x-(12x^2+18x)-3=0

We get rid of parentheses

-12x^2-9x-18x-3=0

We add all the numbers together, and all the variables

-12x^2-27x-3=0

a = -12; b = -27; c = -3;
Δ = b2-4ac
Δ = -272-4·(-12)·(-3)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{65}}{2*-12}=\frac{27-3\sqrt{65}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{65}}{2*-12}=\frac{27+3\sqrt{65}}{-24}
$