2(a+1)=3(a-2)a

Solution for 2(a+1)=3(a-2)a equation:

2(a+1)=3(a-2)a

We move all terms to the left:

2(a+1)-(3(a-2)a)=0

We multiply parentheses

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


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

3(a-2)a

We multiply parentheses

3a^2-6a

Back to the equation:

-(3a^2-6a)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3a^2+8a+2=0

a = -3; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-3)·2
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{-(8)-2\sqrt{22}}{2*-3}=\frac{-8-2\sqrt{22}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*-3}=\frac{-8+2\sqrt{22}}{-6}
$