(24+x)/x=15/9x

Solution for (24+x)/x=15/9x equation:

(24+x)/x=15/9x

We move all terms to the left:

(24+x)/x-(15/9x)=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

(x+24)/x-(+15/9x)=0

We get rid of parentheses

(x+24)/x-15/9x=0

We calculate fractions


(9x^2+216x)/9x^2+(-15x)/9x^2=0

We multiply all the terms by the denominator


(9x^2+216x)+(-15x)=0

We get rid of parentheses

9x^2+216x-15x=0

We add all the numbers together, and all the variables

9x^2+201x=0

a = 9; b = 201; c = 0;
Δ = b2-4ac
Δ = 2012-4·9·0
Δ = 40401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40401}=201$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(201)-201}{2*9}=\frac{-402}{18}
=-22+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+201}{2*9}=\frac{0}{18}
=0
$