x+1/x-1=24

Solution for x+1/x-1=24 equation:

x+1/x-1=24

We move all terms to the left:

x+1/x-1-(24)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-25=0

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}
$