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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+x=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12}
=0
$