3/x+1/5x=1

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

3/x+1/5x=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x/5x^2+x/5x^2-1=0

We multiply all the terms by the denominator


15x+x-1*5x^2=0

We add all the numbers together, and all the variables

16x-1*5x^2=0

Wy multiply elements

-5x^2+16x=0

a = -5; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-5)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-5}=\frac{-32}{-10}
=3+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-5}=\frac{0}{-10}
=0
$