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

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

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

We move all terms to the left:

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


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-2X)+(-20X)+1*5X^2=0

Wy multiply elements

5X^2+(-2X)+(-20X)=0

We get rid of parentheses

5X^2-2X-20X=0

We add all the numbers together, and all the variables

5X^2-22X=0

a = 5; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·5·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*5}=\frac{44}{10}
=4+2/5
$