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

Solution for 9-x^2+9-6x=0 equation:

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

We add all the numbers together, and all the variables

-1x^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}
$