2x+1=x+8/x

Solution for 2x+1=x+8/x equation:

2x+1=x+8/x

We move all terms to the left:

2x+1-(x+8/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+x+8/x)+1=0

We get rid of parentheses

2x-x-8/x+1=0

We multiply all the terms by the denominator


2x*x-x*x+1*x-8=0

We add all the numbers together, and all the variables

x+2x*x-x*x-8=0

Wy multiply elements

2x^2-1x^2+x-8=0

We add all the numbers together, and all the variables

x^2+x-8=0

a = 1; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·1·(-8)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{33}}{2*1}=\frac{-1-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*1}=\frac{-1+\sqrt{33}}{2}
$