X-6/3x+1=x+5/x

Solution for X-6/3x+1=x+5/x equation:

X-6/3X+1=X+5/X

We move all terms to the left:

X-6/3X+1-(X+5/X)=0


Domain of the equation: 3X!=0

X!=0/3

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-6/3X-(+X+5/X)+1=0

We get rid of parentheses

X-6/3X-X-5/X+1=0

We calculate fractions


X-X+(-6X)/3X^2+(-15X)/3X^2+1=0

We add all the numbers together, and all the variables

(-6X)/3X^2+(-15X)/3X^2+1=0

We multiply all the terms by the denominator


(-6X)+(-15X)+1*3X^2=0

Wy multiply elements

3X^2+(-6X)+(-15X)=0

We get rid of parentheses

3X^2-6X-15X=0

We add all the numbers together, and all the variables

3X^2-21X=0

a = 3; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·3·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*3}=\frac{42}{6}
=7
$