X=x^2+9x+9

Solution for X=x^2+9x+9 equation:

X=X^2+9X+9

We move all terms to the left:

X-(X^2+9X+9)=0

We get rid of parentheses

-X^2+X-9X-9=0

We add all the numbers together, and all the variables

-1X^2-8X-9=0

a = -1; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·(-1)·(-9)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*-1}=\frac{8-2\sqrt{7}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*-1}=\frac{8+2\sqrt{7}}{-2}
$