2/5+4/x=1/10x

Solution for 2/5+4/x=1/10x equation:

2/5+4/x=1/10x

We move all terms to the left:

2/5+4/x-(1/10x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/x-1/10x+2/5=0

We calculate fractions


20x^2/250x^2+1000x/250x^2+(-25x)/250x^2=0

We multiply all the terms by the denominator


20x^2+1000x+(-25x)=0

We get rid of parentheses

20x^2+1000x-25x=0

We add all the numbers together, and all the variables

20x^2+975x=0

a = 20; b = 975; c = 0;
Δ = b2-4ac
Δ = 9752-4·20·0
Δ = 950625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{950625}=975$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(975)-975}{2*20}=\frac{-1950}{40}
=-48+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(975)+975}{2*20}=\frac{0}{40}
=0
$