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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


2x/5x^2+(-20x)/5x^2+1+4=0

We add all the numbers together, and all the variables

2x/5x^2+(-20x)/5x^2+5=0

We multiply all the terms by the denominator


2x+(-20x)+5*5x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

25x^2-18x=0

a = 25; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·25·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*25}=\frac{0}{50}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*25}=\frac{36}{50}
=18/25
$