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+54a+3a-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 = 3897
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:

$\sqrt{\Delta}=\sqrt{3897}=\sqrt{9*433}=\sqrt{9}*\sqrt{433}=3\sqrt{433}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{433}}{2*18}=\frac{-57-3\sqrt{433}}{36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{433}}{2*18}=\frac{-57+3\sqrt{433}}{36}
$