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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(x+2)-3

We multiply parentheses

x^2+2x-3

Back to the equation:

-(x^2+2x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+4x+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$