f(-2)=(1/6)^-2

Solution for f(-2)=(1/6)^-2 equation:

f(-2)=(1/6)^-2

We move all terms to the left:

f(-2)-((1/6)^-2)=0

We add all the numbers together, and all the variables

f(-2)-((+1/6)^-2)=0

We multiply parentheses

-2f-((+1/6)^-2)=0

We multiply all the terms by the denominator


-2f*6)^-2)-((+1=0

Wy multiply elements

-12f^2+1=0

a = -12; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-12)·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-12}=\frac{0-4\sqrt{3}}{-24}
=-\frac{4\sqrt{3}}{-24}
=-\frac{\sqrt{3}}{-6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-12}=\frac{0+4\sqrt{3}}{-24}
=\frac{4\sqrt{3}}{-24}
=\frac{\sqrt{3}}{-6}
$