-9=-(x^2-6x-9)

Solution for -9=-(x^2-6x-9) equation:

-9=-(x^2-6x-9)

We move all terms to the left:

-9-(-(x^2-6x-9))=0


We calculate terms in parentheses: -(-(x^2-6x-9)), so:

-(x^2-6x-9)

We get rid of parentheses

-x^2+6x+9

We add all the numbers together, and all the variables

-1x^2+6x+9

Back to the equation:

-(-1x^2+6x+9)


We get rid of parentheses

1x^2-6x-9-9=0

We add all the numbers together, and all the variables

x^2-6x-18=0

a = 1; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·1·(-18)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*1}=\frac{6-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*1}=\frac{6+6\sqrt{3}}{2}
$