3a=2a(a+1)

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

3a=2a(a+1)

We move all terms to the left:

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


We calculate terms in parentheses: -(2a(a+1)), so:

2a(a+1)

We multiply parentheses

2a^2+2a

Back to the equation:

-(2a^2+2a)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2a^2+a=0

a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-2}=\frac{-2}{-4}
=1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-2}=\frac{0}{-4}
=0
$