3x(2x+1)=2(x+1)

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

3x(2x+1)=2(x+1)

We move all terms to the left:

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

We multiply parentheses

6x^2+3x-(2(x+1))=0


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

2(x+1)

We multiply parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+x-2=0

a = 6; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·6·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*6}=\frac{6}{12}
=1/2
$