1/5x+2/x=-4

Solution for 1/5x+2/x=-4 equation:

1/5x+2/x=-4

We move all terms to the left:

1/5x+2/x-(-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+2/x+4=0

We calculate fractions


x/5x^2+10x/5x^2+4=0

We multiply all the terms by the denominator


x+10x+4*5x^2=0

We add all the numbers together, and all the variables

11x+4*5x^2=0

Wy multiply elements

20x^2+11x=0

a = 20; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·20·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*20}=\frac{-22}{40}
=-11/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*20}=\frac{0}{40}
=0
$