(x2+4x)/(x+2)=2x/3

Solution for (x2+4x)/(x+2)=2x/3 equation:

(x2+4x)/(x+2)=2x/3

We move all terms to the left:

(x2+4x)/(x+2)-(2x/3)=0


Domain of the equation: (x+2)!=0

We move all terms containing x to the left, all other terms to the right

x!=-2

x∈R


We add all the numbers together, and all the variables

(+x^2+4x)/(x+2)-(+2x/3)=0

We get rid of parentheses

(+x^2+4x)/(x+2)-2x/3=0

We calculate fractions


(-2x^2-4x)/(3x+6)+(3x^2+12x)/(3x+6)=0

We multiply all the terms by the denominator


(-2x^2-4x)+(3x^2+12x)=0

We get rid of parentheses

-2x^2+3x^2-4x+12x=0

We add all the numbers together, and all the variables

x^2+8x=0

a = 1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*1}=\frac{0}{2}
=0
$