2(3a-2)a=3

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

2(3a-2)a=3

We move all terms to the left:

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

We multiply parentheses

6a^2-4a-3=0

a = 6; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·6·(-3)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*6}=\frac{4-2\sqrt{22}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*6}=\frac{4+2\sqrt{22}}{12}
$