1/3x-2+5/x=0

Solution for 1/3x-2+5/x=0 equation:

1/3x-2+5/x=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


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

16x-2*3x^2=0

Wy multiply elements

-6x^2+16x=0

a = -6; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-6)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-6}=\frac{-32}{-12}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-6}=\frac{0}{-12}
=0
$