a=a(2a+9)

Solution for a=a(2a+9) equation:

a=a(2a+9)

We move all terms to the left:

a-(a(2a+9))=0


We calculate terms in parentheses: -(a(2a+9)), so:

a(2a+9)

We multiply parentheses

2a^2+9a

Back to the equation:

-(2a^2+9a)


We get rid of parentheses

-2a^2+a-9a=0

We add all the numbers together, and all the variables

-2a^2-8a=0

a = -2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-2}=\frac{0}{-4}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-2}=\frac{16}{-4}
=-4
$