4^2x-5=1/16

Solution for 4^2x-5=1/16 equation:

4^2x-5=1/16

We move all terms to the left:

4^2x-5-(1/16)=0

We add all the numbers together, and all the variables

4^2x-5-(+1/16)=0

We get rid of parentheses

4^2x-5-1/16=0

We multiply all the terms by the denominator


4^2x*16-1-5*16=0

We add all the numbers together, and all the variables

4^2x*16-81=0

Wy multiply elements

64x^2-81=0

a = 64; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·64·(-81)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*64}=\frac{-144}{128}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*64}=\frac{144}{128}
=1+1/8
$