X+2/x=54

Solution for X+2/x=54 equation:

X+2/X=54

We move all terms to the left:

X+2/X-(54)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-54*X+2=0

We add all the numbers together, and all the variables

-54X+X*X+2=0

Wy multiply elements

X^2-54X+2=0

a = 1; b = -54; c = +2;
Δ = b2-4ac
Δ = -542-4·1·2
Δ = 2908
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2908}=\sqrt{4*727}=\sqrt{4}*\sqrt{727}=2\sqrt{727}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{727}}{2*1}=\frac{54-2\sqrt{727}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{727}}{2*1}=\frac{54+2\sqrt{727}}{2}
$