4/x-3=5/3x+5

Solution for 4/x-3=5/3x+5 equation:

4/x-3=5/3x+5

We move all terms to the left:

4/x-3-(5/3x+5)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4/x-5/3x-5-3=0

We calculate fractions


12x/3x^2+(-5x)/3x^2-5-3=0

We add all the numbers together, and all the variables

12x/3x^2+(-5x)/3x^2-8=0

We multiply all the terms by the denominator


12x+(-5x)-8*3x^2=0

Wy multiply elements

-24x^2+12x+(-5x)=0

We get rid of parentheses

-24x^2+12x-5x=0

We add all the numbers together, and all the variables

-24x^2+7x=0

a = -24; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-24)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-24}=\frac{-14}{-48}
=7/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-24}=\frac{0}{-48}
=0
$