3/x+13/5x=28/15

Solution for 3/x+13/5x=28/15 equation:

3/x+13/5x=28/15

We move all terms to the left:

3/x+13/5x-(28/15)=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

3/x+13/5x-(+28/15)=0

We get rid of parentheses

3/x+13/5x-28/15=0

We calculate fractions


(-700x^2)/75x^2+225x/75x^2+195x/75x^2=0

We multiply all the terms by the denominator


(-700x^2)+225x+195x=0

We add all the numbers together, and all the variables

(-700x^2)+420x=0

We get rid of parentheses

-700x^2+420x=0

a = -700; b = 420; c = 0;
Δ = b2-4ac
Δ = 4202-4·(-700)·0
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-420}{2*-700}=\frac{-840}{-1400}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+420}{2*-700}=\frac{0}{-1400}
=0
$