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+39a-6=0

a = -18; b = 39; c = -6;
Δ = b2-4ac
Δ = 392-4·(-18)·(-6)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-33}{2*-18}=\frac{-72}{-36}
=+2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+33}{2*-18}=\frac{-6}{-36}
=1/6
$