x/x^2-8=3

Solution for x/x^2-8=3 equation:

x/x^2-8=3

We move all terms to the left:

x/x^2-8-(3)=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^2-11=0

We multiply all the terms by the denominator


x-11*x^2=0

We add all the numbers together, and all the variables

-11x^2+x=0

a = -11; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-11)·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*-11}=\frac{-2}{-22}
=1/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-11}=\frac{0}{-22}
=0
$