2x-5=-1/x

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Solution for 2x-5=-1/x equation: 



2x-5=-1/x

We move all terms to the left:

2x-5-(-1/x)=0



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



We get rid of parentheses

2x+1/x-5=0

We multiply all the terms by the denominator


2x*x-5*x+1=0

We add all the numbers together, and all the variables

-5x+2x*x+1=0

Wy multiply elements

2x^2-5x+1=0

a = 2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·2·1
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{-(-5)-\sqrt{17}}{2*2}=\frac{5-\sqrt{17}}{4}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*2}=\frac{5+\sqrt{17}}{4}
$

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