2(a-6)=4a(2a-12)

Solution for 2(a-6)=4a(2a-12) equation:

2(a-6)=4a(2a-12)

We move all terms to the left:

2(a-6)-(4a(2a-12))=0

We multiply parentheses

2a-(4a(2a-12))-12=0


We calculate terms in parentheses: -(4a(2a-12)), so:

4a(2a-12)

We multiply parentheses

8a^2-48a

Back to the equation:

-(8a^2-48a)


We get rid of parentheses

-8a^2+2a+48a-12=0

We add all the numbers together, and all the variables

-8a^2+50a-12=0

a = -8; b = 50; c = -12;
Δ = b2-4ac
Δ = 502-4·(-8)·(-12)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-46}{2*-8}=\frac{-96}{-16}
=+6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+46}{2*-8}=\frac{-4}{-16}
=1/4
$