9(x-3)=(x+3)(x-3)-2(x+3)

Solution for 9(x-3)=(x+3)(x-3)-2(x+3) equation:

9(x-3)=(x+3)(x-3)-2(x+3)

We move all terms to the left:

9(x-3)-((x+3)(x-3)-2(x+3))=0

We use the square of the difference formula

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

We multiply parentheses

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

We add all the numbers together, and all the variables

x^2+9x-18=0

a = 1; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·1·(-18)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*1}=\frac{-9-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*1}=\frac{-9+3\sqrt{17}}{2}
$