F(x)=1/16^x2

Solution for F(x)=1/16^x2 equation:

(F)=1/16^F2

We move all terms to the left:

(F)-(1/16^F2)=0


Domain of the equation: 16^F2)!=0

F!=0/1

F!=0

F∈R


We get rid of parentheses

F-1/16^F2=0

We multiply all the terms by the denominator


F*16^F2-1=0

Wy multiply elements

16F^2-1=0

a = 16; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·16·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*16}=\frac{-8}{32}
=-1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*16}=\frac{8}{32}
=1/4
$