3(a-2)=6a(3a+6)

Solution for 3(a-2)=6a(3a+6) equation:

3(a-2)=6a(3a+6)

We move all terms to the left:

3(a-2)-(6a(3a+6))=0

We multiply parentheses

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


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

6a(3a+6)

We multiply parentheses

18a^2+36a

Back to the equation:

-(18a^2+36a)


We get rid of parentheses

-18a^2+3a-36a-6=0

We add all the numbers together, and all the variables

-18a^2-33a-6=0

a = -18; b = -33; c = -6;
Δ = b2-4ac
Δ = -332-4·(-18)·(-6)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{73}}{2*-18}=\frac{33-3\sqrt{73}}{-36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{73}}{2*-18}=\frac{33+3\sqrt{73}}{-36}
$