3x/x+1=5/2x

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

3x/x+1=5/2x

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


6x^2/2x^2+(-5x)/2x^2+1=0

We multiply all the terms by the denominator


6x^2+(-5x)+1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-5x=0

a = 8; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·8·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*8}=\frac{10}{16}
=5/8
$