X=5+4/x

Solution for X=5+4/x equation:

X=5+4/X

We move all terms to the left:

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

We get rid of parentheses

X-4/X-5=0

We multiply all the terms by the denominator


X*X-5*X-4=0

We add all the numbers together, and all the variables

-5X+X*X-4=0

Wy multiply elements

X^2-5X-4=0

a = 1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·1·(-4)
Δ = 41
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{-(-5)-\sqrt{41}}{2*1}=\frac{5-\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*1}=\frac{5+\sqrt{41}}{2}
$