X+1/x=25

Solution for X+1/x=25 equation:

X+1/X=25

We move all terms to the left:

X+1/X-(25)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-25*X+1=0

We add all the numbers together, and all the variables

-25X+X*X+1=0

Wy multiply elements

X^2-25X+1=0

a = 1; b = -25; c = +1;
Δ = b2-4ac
Δ = -252-4·1·1
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{69}}{2*1}=\frac{25-3\sqrt{69}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{69}}{2*1}=\frac{25+3\sqrt{69}}{2}
$