x+3/x-1=25

Solution for x+3/x-1=25 equation:

x+3/x-1=25

We move all terms to the left:

x+3/x-1-(25)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-26=0

We multiply all the terms by the denominator


x*x-26*x+3=0

We add all the numbers together, and all the variables

-26x+x*x+3=0

Wy multiply elements

x^2-26x+3=0

a = 1; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·1·3
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{166}}{2*1}=\frac{26-2\sqrt{166}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{166}}{2*1}=\frac{26+2\sqrt{166}}{2}
$