7/x+2=1/9x

Solution for 7/x+2=1/9x equation:

7/x+2=1/9x

We move all terms to the left:

7/x+2-(1/9x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/x-(+1/9x)+2=0

We get rid of parentheses

7/x-1/9x+2=0

We calculate fractions


63x/9x^2+(-x)/9x^2+2=0

We add all the numbers together, and all the variables

63x/9x^2+(-1x)/9x^2+2=0

We multiply all the terms by the denominator


63x+(-1x)+2*9x^2=0

Wy multiply elements

18x^2+63x+(-1x)=0

We get rid of parentheses

18x^2+63x-1x=0

We add all the numbers together, and all the variables

18x^2+62x=0

a = 18; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·18·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*18}=\frac{-124}{36}
=-3+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*18}=\frac{0}{36}
=0
$