6/x^2+1=7

Solution for 6/x^2+1=7 equation:

6/x^2+1=7

We move all terms to the left:

6/x^2+1-(7)=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

6/x^2-6=0

We multiply all the terms by the denominator


-6*x^2+6=0

We add all the numbers together, and all the variables

-6x^2+6=0

a = -6; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-6)·6
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-6}=\frac{12}{-12}
=-1
$