X=y2+y2-9y-9

Solution for X=y2+y2-9y-9 equation:

X=X2+X2-9X-9

We move all terms to the left:

X-(X2+X2-9X-9)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2X^2+10X+9=0

a = -2; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-2)·9
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*-2}=\frac{-10-2\sqrt{43}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*-2}=\frac{-10+2\sqrt{43}}{-4}
$