6a+12=2a(4a-8)

Solution for 6a+12=2a(4a-8) equation:

6a+12=2a(4a-8)

We move all terms to the left:

6a+12-(2a(4a-8))=0


We calculate terms in parentheses: -(2a(4a-8)), so:

2a(4a-8)

We multiply parentheses

8a^2-16a

Back to the equation:

-(8a^2-16a)


We get rid of parentheses

-8a^2+6a+16a+12=0

We add all the numbers together, and all the variables

-8a^2+22a+12=0

a = -8; b = 22; c = +12;
Δ = b2-4ac
Δ = 222-4·(-8)·12
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{217}}{2*-8}=\frac{-22-2\sqrt{217}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{217}}{2*-8}=\frac{-22+2\sqrt{217}}{-16}
$