X+3/x-16/15=x-3/3x

Solution for X+3/x-16/15=x-3/3x equation:

X+3/X-16/15=X-3/3X

We move all terms to the left:

X+3/X-16/15-(X-3/3X)=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

X+3/X-(+X-3/3X)-16/15=0

We get rid of parentheses

X+3/X-X+3/3X-16/15=0

We calculate fractions


(-144X^2)/45X^2+X-X+135X/45X^2+45X/45X^2=0

We add all the numbers together, and all the variables

(-144X^2)/45X^2+135X/45X^2+45X/45X^2=0

We multiply all the terms by the denominator


(-144X^2)+135X+45X=0

We add all the numbers together, and all the variables

(-144X^2)+180X=0

We get rid of parentheses

-144X^2+180X=0

a = -144; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-144)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-144}=\frac{-360}{-288}
=1+1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-144}=\frac{0}{-288}
=0
$