3/x-3=9/5x-6

Solution for 3/x-3=9/5x-6 equation:

3/x-3=9/5x-6

We move all terms to the left:

3/x-3-(9/5x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-6)!=0

x∈R


We get rid of parentheses

3/x-9/5x+6-3=0

We calculate fractions


15x/5x^2+(-9x)/5x^2+6-3=0

We add all the numbers together, and all the variables

15x/5x^2+(-9x)/5x^2+3=0

We multiply all the terms by the denominator


15x+(-9x)+3*5x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+6x=0

a = 15; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·15·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*15}=\frac{-12}{30}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*15}=\frac{0}{30}
=0
$