3x/9x=15/x

Solution for 3x/9x=15/x equation:

3x/9x=15/x

We move all terms to the left:

3x/9x-(15/x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x/9x-(+15/x)=0

We get rid of parentheses

3x/9x-15/x=0

We calculate fractions


3x^2/9x^2+(-135x)/9x^2=0

We multiply all the terms by the denominator


3x^2+(-135x)=0

We get rid of parentheses

3x^2-135x=0

a = 3; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·3·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*3}=\frac{270}{6}
=45
$