5/2x+3=1/x

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

5/2x+3=1/x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+3x=0

a = 6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*6}=\frac{0}{12}
=0
$