(3/x+3)+(4x/2x+6)=0

Solution for (3/x+3)+(4x/2x+6)=0 equation:

(3/x+3)+(4x/2x+6)=0


Domain of the equation: x+3)!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

3/x+4x/2x+3+6=0

We calculate fractions


4x^2/2x^2+6x/2x^2+3+6=0

We add all the numbers together, and all the variables

4x^2/2x^2+6x/2x^2+9=0

We multiply all the terms by the denominator


4x^2+6x+9*2x^2=0

Wy multiply elements

4x^2+18x^2+6x=0

We add all the numbers together, and all the variables

22x^2+6x=0

a = 22; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·22·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*22}=\frac{-12}{44}
=-3/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*22}=\frac{0}{44}
=0
$