F(-10)=x/x^2-16

Solution for F(-10)=x/x^2-16 equation:

(-10)=F/F^2-16

We move all terms to the left:

(-10)-(F/F^2-16)=0


Domain of the equation: F^2-16)!=0

F∈R


We add all the numbers together, and all the variables

-(F/F^2-16)-10=0

We get rid of parentheses

-F/F^2+16-10=0

We multiply all the terms by the denominator


-F+16*F^2-10*F^2=0

We add all the numbers together, and all the variables

6F^2-1F=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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