F(3)=1/x2-121

Solution for F(3)=1/x2-121 equation:

(3)=1/F2-121

We move all terms to the left:

(3)-(1/F2-121)=0


Domain of the equation: F2-121)!=0

F∈R


We get rid of parentheses

-1/F2+121+3=0

We multiply all the terms by the denominator


121*F2+3*F2-1=0

We add all the numbers together, and all the variables

124F^2-1=0

a = 124; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·124·(-1)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{31}}{2*124}=\frac{0-4\sqrt{31}}{248}
=-\frac{4\sqrt{31}}{248}
=-\frac{\sqrt{31}}{62}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{31}}{2*124}=\frac{0+4\sqrt{31}}{248}
=\frac{4\sqrt{31}}{248}
=\frac{\sqrt{31}}{62}
$