2/x+1=3x/5x-1

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

2/x+1=3x/5x-1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-3x^2)/5x^2+10x/5x^2+1+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-3x^2)+10x+2*5x^2=0

Wy multiply elements

(-3x^2)+10x^2+10x=0

We get rid of parentheses

-3x^2+10x^2+10x=0

We add all the numbers together, and all the variables

7x^2+10x=0

a = 7; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·7·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*7}=\frac{-20}{14}
=-1+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*7}=\frac{0}{14}
=0
$