6a+12=2(3a-8)6a

Solution for 6a+12=2(3a-8)6a equation:

6a+12=2(3a-8)6a

We move all terms to the left:

6a+12-(2(3a-8)6a)=0


We calculate terms in parentheses: -(2(3a-8)6a), so:

2(3a-8)6a

We multiply parentheses

36a^2-96a

Back to the equation:

-(36a^2-96a)


We get rid of parentheses

-36a^2+6a+96a+12=0

We add all the numbers together, and all the variables

-36a^2+102a+12=0

a = -36; b = 102; c = +12;
Δ = b2-4ac
Δ = 1022-4·(-36)·12
Δ = 12132
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:

$\sqrt{\Delta}=\sqrt{12132}=\sqrt{36*337}=\sqrt{36}*\sqrt{337}=6\sqrt{337}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{337}}{2*-36}=\frac{-102-6\sqrt{337}}{-72}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{337}}{2*-36}=\frac{-102+6\sqrt{337}}{-72}
$