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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


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

(+x^2+2x-1x-2)

We get rid of parentheses

x^2+2x-1x-2

We add all the numbers together, and all the variables

x^2+x-2

Back to the equation:

-(x^2+x-2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x+2=0

a = 2; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*2}=\frac{-2}{4}
=-1/2
$