5+13/x+1/5=7/2x

Solution for 5+13/x+1/5=7/2x equation:

5+13/x+1/5=7/2x

We move all terms to the left:

5+13/x+1/5-(7/2x)=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

13/x-(+7/2x)+5+1/5=0

We get rid of parentheses

13/x-7/2x+5+1/5=0

We calculate fractions


4x^2/50x^2+650x/50x^2+(-175x)/50x^2+5=0

We multiply all the terms by the denominator


4x^2+650x+(-175x)+5*50x^2=0

Wy multiply elements

4x^2+250x^2+650x+(-175x)=0

We get rid of parentheses

4x^2+250x^2+650x-175x=0

We add all the numbers together, and all the variables

254x^2+475x=0

a = 254; b = 475; c = 0;
Δ = b2-4ac
Δ = 4752-4·254·0
Δ = 225625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225625}=475$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(475)-475}{2*254}=\frac{-950}{508}
=-1+221/254
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(475)+475}{2*254}=\frac{0}{508}
=0
$