0=x(x+9)

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

0=x(x+9)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x^2-9x=0

a = -1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-1}=\frac{18}{-2}
=-9
$