12x-x^2=x^2+9

Solution for 12x-x^2=x^2+9 equation:

12x-x^2=x^2+9

We move all terms to the left:

12x-x^2-(x^2+9)=0

We add all the numbers together, and all the variables

-1x^2+12x-(x^2+9)=0

We get rid of parentheses

-1x^2-x^2+12x-9=0

We add all the numbers together, and all the variables

-2x^2+12x-9=0

a = -2; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·(-2)·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*-2}=\frac{-12-6\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*-2}=\frac{-12+6\sqrt{2}}{-4}
$