8/x-9/5=3/7x

Solution for 8/x-9/5=3/7x equation:

8/x-9/5=3/7x

We move all terms to the left:

8/x-9/5-(3/7x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/x-(+3/7x)-9/5=0

We get rid of parentheses

8/x-3/7x-9/5=0

We calculate fractions


(-441x^2)/175x^2+1400x/175x^2+(-75x)/175x^2=0

We multiply all the terms by the denominator


(-441x^2)+1400x+(-75x)=0

We get rid of parentheses

-441x^2+1400x-75x=0

We add all the numbers together, and all the variables

-441x^2+1325x=0

a = -441; b = 1325; c = 0;
Δ = b2-4ac
Δ = 13252-4·(-441)·0
Δ = 1755625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1755625}=1325$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1325)-1325}{2*-441}=\frac{-2650}{-882}
=3+2/441
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1325)+1325}{2*-441}=\frac{0}{-882}
=0
$