1/2+2/x=13/3x

Solution for 1/2+2/x=13/3x equation:

1/2+2/x=13/3x

We move all terms to the left:

1/2+2/x-(13/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(+13/3x)+1/2=0

We get rid of parentheses

2/x-13/3x+1/2=0

We calculate fractions


9x^2/12x^2+24x/12x^2+(-52x)/12x^2=0

We multiply all the terms by the denominator


9x^2+24x+(-52x)=0

We get rid of parentheses

9x^2+24x-52x=0

We add all the numbers together, and all the variables

9x^2-28x=0

a = 9; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·9·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*9}=\frac{56}{18}
=3+1/9
$