2/5x+(x+1)/x=2

Solution for 2/5x+(x+1)/x=2 equation:

2/5x+(x+1)/x=2

We move all terms to the left:

2/5x+(x+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


2x/5x^2+(5x^2+5x)/5x^2-2=0

We multiply all the terms by the denominator


2x+(5x^2+5x)-2*5x^2=0

Wy multiply elements

-10x^2+2x+(5x^2+5x)=0

We get rid of parentheses

-10x^2+5x^2+2x+5x=0

We add all the numbers together, and all the variables

-5x^2+7x=0

a = -5; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-5)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-5}=\frac{0}{-10}
=0
$