3/5x+1/x=2

Solution for 3/5x+1/x=2 equation:

3/5x+1/x=2

We move all terms to the left:

3/5x+1/x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


3x/5x^2+5x/5x^2-2=0

We multiply all the terms by the denominator


3x+5x-2*5x^2=0

We add all the numbers together, and all the variables

8x-2*5x^2=0

Wy multiply elements

-10x^2+8x=0

a = -10; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-10)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-10}=\frac{-16}{-20}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-10}=\frac{0}{-20}
=0
$