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

Solution for (1/x+2)+(5/3x-2)=4 equation:

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

We move all terms to the left:

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


Domain of the equation: x+2)!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3x+5x-4*3x^2=0

We add all the numbers together, and all the variables

8x-4*3x^2=0

Wy multiply elements

-12x^2+8x=0

a = -12; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-12)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-12}=\frac{-16}{-24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-12}=\frac{0}{-24}
=0
$