0=11(x-9)+x(x-9)

Solution for 0=11(x-9)+x(x-9) equation:

0=11(x-9)+x(x-9)

We move all terms to the left:

0-(11(x-9)+x(x-9))=0

We add all the numbers together, and all the variables

-(11(x-9)+x(x-9))=0


We calculate terms in parentheses: -(11(x-9)+x(x-9)), so:

11(x-9)+x(x-9)

We multiply parentheses

x^2+11x-9x-99

We add all the numbers together, and all the variables

x^2+2x-99

Back to the equation:

-(x^2+2x-99)


We get rid of parentheses

-x^2-2x+99=0

We add all the numbers together, and all the variables

-1x^2-2x+99=0

a = -1; b = -2; c = +99;
Δ = b2-4ac
Δ = -22-4·(-1)·99
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-20}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+20}{2*-1}=\frac{22}{-2}
=-11
$