4^2x=3/32

Solution for 4^2x=3/32 equation:

4^2x=3/32

We move all terms to the left:

4^2x-(3/32)=0

We add all the numbers together, and all the variables

4^2x-(+3/32)=0

We get rid of parentheses

4^2x-3/32=0

We multiply all the terms by the denominator


4^2x*32-3=0

Wy multiply elements

128x^2-3=0

a = 128; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·128·(-3)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*128}=\frac{0-16\sqrt{6}}{256}
=-\frac{16\sqrt{6}}{256}
=-\frac{\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*128}=\frac{0+16\sqrt{6}}{256}
=\frac{16\sqrt{6}}{256}
=\frac{\sqrt{6}}{16}
$