Q(0)=1/x^2-9

Solution for Q(0)=1/x^2-9 equation:

(0)=1/Q^2-9

We move all terms to the left:

(0)-(1/Q^2-9)=0


Domain of the equation: Q^2-9)!=0

Q∈R


We add all the numbers together, and all the variables

-(1/Q^2-9)=0

We get rid of parentheses

-1/Q^2+9=0

We multiply all the terms by the denominator


9*Q^2-1=0

We add all the numbers together, and all the variables

9Q^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$