2/x+3/5x=13/10

Solution for 2/x+3/5x=13/10 equation:

2/x+3/5x=13/10

We move all terms to the left:

2/x+3/5x-(13/10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+3/5x-(+13/10)=0

We get rid of parentheses

2/x+3/5x-13/10=0

We calculate fractions


(-325x^2)/50x^2+100x/50x^2+30x/50x^2=0

We multiply all the terms by the denominator


(-325x^2)+100x+30x=0

We add all the numbers together, and all the variables

(-325x^2)+130x=0

We get rid of parentheses

-325x^2+130x=0

a = -325; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·(-325)·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*-325}=\frac{-260}{-650}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*-325}=\frac{0}{-650}
=0
$