4a-3(a-2)=2(3a2)

Solution for 4a-3(a-2)=2(3a2) equation:

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

We move all terms to the left:

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

determiningTheFunctionDomain
4a-3(a-2)-23a^2=0

We add all the numbers together, and all the variables

-23a^2+4a-3(a-2)=0

We multiply parentheses

-23a^2+4a-3a+6=0

We add all the numbers together, and all the variables

-23a^2+a+6=0

a = -23; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-23)·6
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{553}}{2*-23}=\frac{-1-\sqrt{553}}{-46}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{553}}{2*-23}=\frac{-1+\sqrt{553}}{-46}
$