X/x^2-6=1

Solution for X/x^2-6=1 equation:

X/X^2-6=1

We move all terms to the left:

X/X^2-6-(1)=0


Domain of the equation: X^2!=0

X^2!=0/

X^2!=√0

X!=0

X∈R


We add all the numbers together, and all the variables

X/X^2-7=0

We multiply all the terms by the denominator


X-7*X^2=0

We add all the numbers together, and all the variables

-7X^2+X=0

a = -7; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-7)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-7}=\frac{-2}{-14}
=1/7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-7}=\frac{0}{-14}
=0
$