X^2/x-5=25/x-5

Solution for X^2/x-5=25/x-5 equation:

X^2/X-5=25/X-5

We move all terms to the left:

X^2/X-5-(25/X-5)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-5)!=0

X∈R


We get rid of parentheses

X^2/X-25/X+5-5=0

We multiply all the terms by the denominator


X^2+5*X-5*X-25=0

We add all the numbers together, and all the variables

X^2-25=0

a = 1; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·1·(-25)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*1}=\frac{10}{2}
=5
$