9/x=10/3x+5

Solution for 9/x=10/3x+5 equation:

9/x=10/3x+5

We move all terms to the left:

9/x-(10/3x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

9/x-10/3x-5=0

We calculate fractions


27x/3x^2+(-10x)/3x^2-5=0

We multiply all the terms by the denominator


27x+(-10x)-5*3x^2=0

Wy multiply elements

-15x^2+27x+(-10x)=0

We get rid of parentheses

-15x^2+27x-10x=0

We add all the numbers together, and all the variables

-15x^2+17x=0

a = -15; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-15)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-15}=\frac{-34}{-30}
=1+2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-15}=\frac{0}{-30}
=0
$