0=9x(x+6)

Solution for 0=9x(x+6) equation:

0=9x(x+6)

We move all terms to the left:

0-(9x(x+6))=0

We add all the numbers together, and all the variables

-(9x(x+6))=0


We calculate terms in parentheses: -(9x(x+6)), so:

9x(x+6)

We multiply parentheses

9x^2+54x

Back to the equation:

-(9x^2+54x)


We get rid of parentheses

-9x^2-54x=0

a = -9; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·(-9)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*-9}=\frac{108}{-18}
=-6
$