2/x+16/15=19/3x

Solution for 2/x+16/15=19/3x equation:

2/x+16/15=19/3x

We move all terms to the left:

2/x+16/15-(19/3x)=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-(+19/3x)+16/15=0

We get rid of parentheses

2/x-19/3x+16/15=0

We calculate fractions


144x^2/45x^2+90x/45x^2+(-285x)/45x^2=0

We multiply all the terms by the denominator


144x^2+90x+(-285x)=0

We get rid of parentheses

144x^2+90x-285x=0

We add all the numbers together, and all the variables

144x^2-195x=0

a = 144; b = -195; c = 0;
Δ = b2-4ac
Δ = -1952-4·144·0
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-195}{2*144}=\frac{0}{288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+195}{2*144}=\frac{390}{288}
=1+17/48
$