5/x-1=10/3x-4

Solution for 5/x-1=10/3x-4 equation:

5/x-1=10/3x-4

We move all terms to the left:

5/x-1-(10/3x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

5/x-10/3x+4-1=0

We calculate fractions


15x/3x^2+(-10x)/3x^2+4-1=0

We add all the numbers together, and all the variables

15x/3x^2+(-10x)/3x^2+3=0

We multiply all the terms by the denominator


15x+(-10x)+3*3x^2=0

Wy multiply elements

9x^2+15x+(-10x)=0

We get rid of parentheses

9x^2+15x-10x=0

We add all the numbers together, and all the variables

9x^2+5x=0

a = 9; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·9·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*9}=\frac{-10}{18}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*9}=\frac{0}{18}
=0
$