16^2x=1/4

Solution for 16^2x=1/4 equation:

16^2x=1/4

We move all terms to the left:

16^2x-(1/4)=0

We add all the numbers together, and all the variables

16^2x-(+1/4)=0

We get rid of parentheses

16^2x-1/4=0

We multiply all the terms by the denominator


16^2x*4-1=0

Wy multiply elements

64x^2-1=0

a = 64; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·64·(-1)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*64}=\frac{-16}{128}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*64}=\frac{16}{128}
=1/8
$