X-6/4x+1=x+2/x

Solution for X-6/4x+1=x+2/x equation:

X-6/4X+1=X+2/X

We move all terms to the left:

X-6/4X+1-(X+2/X)=0


Domain of the equation: 4X!=0

X!=0/4

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-6/4X-(+X+2/X)+1=0

We get rid of parentheses

X-6/4X-X-2/X+1=0

We calculate fractions


X-X+(-6X)/4X^2+(-8X)/4X^2+1=0

We add all the numbers together, and all the variables

(-6X)/4X^2+(-8X)/4X^2+1=0

We multiply all the terms by the denominator


(-6X)+(-8X)+1*4X^2=0

Wy multiply elements

4X^2+(-6X)+(-8X)=0

We get rid of parentheses

4X^2-6X-8X=0

We add all the numbers together, and all the variables

4X^2-14X=0

a = 4; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·4·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*4}=\frac{28}{8}
=3+1/2
$