11^2=x*(x+9)

Solution for 11^2=x*(x+9) equation:

11^2=x(x+9)

We move all terms to the left:

11^2-(x(x+9))=0

We add all the numbers together, and all the variables

-(x(x+9))+121=0


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

x(x+9)

We multiply parentheses

x^2+9x

Back to the equation:

-(x^2+9x)


We get rid of parentheses

-x^2-9x+121=0

We add all the numbers together, and all the variables

-1x^2-9x+121=0

a = -1; b = -9; c = +121;
Δ = b2-4ac
Δ = -92-4·(-1)·121
Δ = 565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{565}}{2*-1}=\frac{9-\sqrt{565}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{565}}{2*-1}=\frac{9+\sqrt{565}}{-2}
$