2/3x+5/x=17

Solution for 2/3x+5/x=17 equation:

2/3x+5/x=17

We move all terms to the left:

2/3x+5/x-(17)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


2x/3x^2+15x/3x^2-17=0

We multiply all the terms by the denominator


2x+15x-17*3x^2=0

We add all the numbers together, and all the variables

17x-17*3x^2=0

Wy multiply elements

-51x^2+17x=0

a = -51; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-51)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-51}=\frac{-34}{-102}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-51}=\frac{0}{-102}
=0
$