3(a-3)=6a(3a-9)

Solution for 3(a-3)=6a(3a-9) equation:

3(a-3)=6a(3a-9)

We move all terms to the left:

3(a-3)-(6a(3a-9))=0

We multiply parentheses

3a-(6a(3a-9))-9=0


We calculate terms in parentheses: -(6a(3a-9)), so:

6a(3a-9)

We multiply parentheses

18a^2-54a

Back to the equation:

-(18a^2-54a)


We get rid of parentheses

-18a^2+3a+54a-9=0

We add all the numbers together, and all the variables

-18a^2+57a-9=0

a = -18; b = 57; c = -9;
Δ = b2-4ac
Δ = 572-4·(-18)·(-9)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-51}{2*-18}=\frac{-108}{-36}
=+3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+51}{2*-18}=\frac{-6}{-36}
=1/6
$