a=2a(3a-4)

Solution for a=2a(3a-4) equation:

a=2a(3a-4)

We move all terms to the left:

a-(2a(3a-4))=0


We calculate terms in parentheses: -(2a(3a-4)), so:

2a(3a-4)

We multiply parentheses

6a^2-8a

Back to the equation:

-(6a^2-8a)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-6a^2+9a=0

a = -6; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-6)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-6}=\frac{0}{-12}
=0
$