7/x+2=9/3x+6

Solution for 7/x+2=9/3x+6 equation:

7/x+2=9/3x+6

We move all terms to the left:

7/x+2-(9/3x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

7/x-9/3x-6+2=0

We calculate fractions


21x/3x^2+(-9x)/3x^2-6+2=0

We add all the numbers together, and all the variables

21x/3x^2+(-9x)/3x^2-4=0

We multiply all the terms by the denominator


21x+(-9x)-4*3x^2=0

Wy multiply elements

-12x^2+21x+(-9x)=0

We get rid of parentheses

-12x^2+21x-9x=0

We add all the numbers together, and all the variables

-12x^2+12x=0

a = -12; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-12)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-12}=\frac{-24}{-24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-12}=\frac{0}{-24}
=0
$