F(-6)=-24/x^2

Solution for F(-6)=-24/x^2 equation:

(-6)=-24/F^2

We move all terms to the left:

(-6)-(-24/F^2)=0


Domain of the equation: F^2)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

-(-24/F^2)-6=0

We get rid of parentheses

24/F^2-6=0

We multiply all the terms by the denominator


-6*F^2+24=0

We add all the numbers together, and all the variables

-6F^2+24=0

a = -6; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-6)·24
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-6}=\frac{-24}{-12}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-6}=\frac{24}{-12}
=-2
$