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^2-51a-9=0

a = -18; b = -51; c = -9;
Δ = b2-4ac
Δ = -512-4·(-18)·(-9)
Δ = 1953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{217}}{2*-18}=\frac{51-3\sqrt{217}}{-36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{217}}{2*-18}=\frac{51+3\sqrt{217}}{-36}
$