X+2=5+2/x

Solution for X+2=5+2/x equation:

X+2=5+2/X

We move all terms to the left:

X+2-(5+2/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

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

We get rid of parentheses

X-2/X-5+2=0

We multiply all the terms by the denominator


X*X-5*X+2*X-2=0

We add all the numbers together, and all the variables

-3X+X*X-2=0

Wy multiply elements

X^2-3X-2=0

a = 1; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·1·(-2)
Δ = 17
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{-(-3)-\sqrt{17}}{2*1}=\frac{3-\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*1}=\frac{3+\sqrt{17}}{2}
$