3/x+(5)/(x+2)=2

Solution for 3/x+(5)/(x+2)=2 equation:

3/x+(5)/(x+2)=2

We move all terms to the left:

3/x+(5)/(x+2)-(2)=0


Domain of the equation: x!=0

x∈R



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 calculate fractions


(3x+6)/(x^2+2x)+5x/(x^2+2x)-2=0

We multiply all the terms by the denominator


(3x+6)+5x-2*(x^2+2x)=0

We add all the numbers together, and all the variables

5x+(3x+6)-2*(x^2+2x)=0

We multiply parentheses

-2x^2+5x+(3x+6)-4x=0

We get rid of parentheses

-2x^2+5x+3x-4x+6=0

We add all the numbers together, and all the variables

-2x^2+4x+6=0

a = -2; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-2)·6
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{-(4)-8}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-2}=\frac{4}{-4}
=-1
$