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

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

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

We move all terms to the left:

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

We calculate fractions


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

We add all the numbers together, and all the variables

9x/3x^2+(-4x)/3x^2-6=0

We multiply all the terms by the denominator


9x+(-4x)-6*3x^2=0

Wy multiply elements

-18x^2+9x+(-4x)=0

We get rid of parentheses

-18x^2+9x-4x=0

We add all the numbers together, and all the variables

-18x^2+5x=0

a = -18; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-18)·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*-18}=\frac{-10}{-36}
=5/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-18}=\frac{0}{-36}
=0
$