4,25=x+1/x

Solution for 4,25=x+1/x equation:

4.25=x+1/x

We move all terms to the left:

4.25-(x+1/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+1/x)+4.25=0

We get rid of parentheses

-x-1/x+4.25=0

We multiply all the terms by the denominator


-x*x+(4.25)*x-1=0

We multiply parentheses

-x*x+4.25x-1=0

Wy multiply elements

-1x^2+4.25x-1=0

a = -1; b = 4.25; c = -1;
Δ = b2-4ac
Δ = 4.252-4·(-1)·(-1)
Δ = 14.0625
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{-(4.25)-\sqrt{14.0625}}{2*-1}=\frac{-4.25-\sqrt{14.0625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.25)+\sqrt{14.0625}}{2*-1}=\frac{-4.25+\sqrt{14.0625}}{-2}
$