5/3x+6/x-2=35/3x

Solution for 5/3x+6/x-2=35/3x equation:

5/3x+6/x-2=35/3x

We move all terms to the left:

5/3x+6/x-2-(35/3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

5/3x+6/x-(+35/3x)-2=0

We get rid of parentheses

5/3x+6/x-35/3x-2=0

We calculate fractions


(-35x+5)/3x^2+18x/3x^2-2=0

We multiply all the terms by the denominator


(-35x+5)+18x-2*3x^2=0

We add all the numbers together, and all the variables

18x+(-35x+5)-2*3x^2=0

Wy multiply elements

-6x^2+18x+(-35x+5)=0

We get rid of parentheses

-6x^2+18x-35x+5=0

We add all the numbers together, and all the variables

-6x^2-17x+5=0

a = -6; b = -17; c = +5;
Δ = b2-4ac
Δ = -172-4·(-6)·5
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{409}}{2*-6}=\frac{17-\sqrt{409}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{409}}{2*-6}=\frac{17+\sqrt{409}}{-12}
$