X+1/x=2.5

Solution for X+1/x=2.5 equation:

X+1/X=2.5

We move all terms to the left:

X+1/X-(2.5)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+1/X-2.5=0

We multiply all the terms by the denominator


X*X-(2.5)*X+1=0

We multiply parentheses

X*X-2.5X+1=0

Wy multiply elements

X^2-2.5X+1=0

a = 1; b = -2.5; c = +1;
Δ = b2-4ac
Δ = -2.52-4·1·1
Δ = 2.25
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{-(-2.5)-\sqrt{2.25}}{2*1}=\frac{2.5-\sqrt{2.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{2.25}}{2*1}=\frac{2.5+\sqrt{2.25}}{2}
$