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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-12x=0

a = 1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·1·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*1}=\frac{24}{2}
=12
$