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

Solution for 2/x+1+3/5x+1=0 equation:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


10x/5x^2+3x/5x^2+2=0

We multiply all the terms by the denominator


10x+3x+2*5x^2=0

We add all the numbers together, and all the variables

13x+2*5x^2=0

Wy multiply elements

10x^2+13x=0

a = 10; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·10·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*10}=\frac{-26}{20}
=-1+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*10}=\frac{0}{20}
=0
$