2x-1/x=54

Solution for 2x-1/x=54 equation:

2x-1/x=54

We move all terms to the left:

2x-1/x-(54)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-54*x-1=0

We add all the numbers together, and all the variables

-54x+2x*x-1=0

Wy multiply elements

2x^2-54x-1=0

a = 2; b = -54; c = -1;
Δ = b2-4ac
Δ = -542-4·2·(-1)
Δ = 2924
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:

$\sqrt{\Delta}=\sqrt{2924}=\sqrt{4*731}=\sqrt{4}*\sqrt{731}=2\sqrt{731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{731}}{2*2}=\frac{54-2\sqrt{731}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{731}}{2*2}=\frac{54+2\sqrt{731}}{4}
$