3/x+5=3/2x

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

3/x+5=3/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


6x+(-3x)+5*2x^2=0

Wy multiply elements

10x^2+6x+(-3x)=0

We get rid of parentheses

10x^2+6x-3x=0

We add all the numbers together, and all the variables

10x^2+3x=0

a = 10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·10·0
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*10}=\frac{-6}{20}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*10}=\frac{0}{20}
=0
$