4/3x+1=2/x-4

Solution for 4/3x+1=2/x-4 equation:

4/3x+1=2/x-4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/3x-2/x+4+1=0

We calculate fractions


4x/3x^2+(-6x)/3x^2+4+1=0

We add all the numbers together, and all the variables

4x/3x^2+(-6x)/3x^2+5=0

We multiply all the terms by the denominator


4x+(-6x)+5*3x^2=0

Wy multiply elements

15x^2+4x+(-6x)=0

We get rid of parentheses

15x^2+4x-6x=0

We add all the numbers together, and all the variables

15x^2-2x=0

a = 15; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·15·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*15}=\frac{4}{30}
=2/15
$