4^2x-3=1/64

Solution for 4^2x-3=1/64 equation:

4^2x-3=1/64

We move all terms to the left:

4^2x-3-(1/64)=0

We add all the numbers together, and all the variables

4^2x-3-(+1/64)=0

We get rid of parentheses

4^2x-3-1/64=0

We multiply all the terms by the denominator


4^2x*64-1-3*64=0

We add all the numbers together, and all the variables

4^2x*64-193=0

Wy multiply elements

256x^2-193=0

a = 256; b = 0; c = -193;
Δ = b2-4ac
Δ = 02-4·256·(-193)
Δ = 197632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{197632}=\sqrt{1024*193}=\sqrt{1024}*\sqrt{193}=32\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{193}}{2*256}=\frac{0-32\sqrt{193}}{512}
=-\frac{32\sqrt{193}}{512}
=-\frac{\sqrt{193}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{193}}{2*256}=\frac{0+32\sqrt{193}}{512}
=\frac{32\sqrt{193}}{512}
=\frac{\sqrt{193}}{16}
$