3/x-5=2/3x+4

Solution for 3/x-5=2/3x+4 equation:

3/x-5=2/3x+4

We move all terms to the left:

3/x-5-(2/3x+4)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

3/x-2/3x-4-5=0

We calculate fractions


9x/3x^2+(-2x)/3x^2-4-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-27x^2+9x+(-2x)=0

We get rid of parentheses

-27x^2+9x-2x=0

We add all the numbers together, and all the variables

-27x^2+7x=0

a = -27; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-27)·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*-27}=\frac{-14}{-54}
=7/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-27}=\frac{0}{-54}
=0
$