1/2=4^2x-1

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

1/2=4^2x-1

We move all terms to the left:

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

We get rid of parentheses

-4^2x+1+1/2=0

We multiply all the terms by the denominator


-4^2x*2+1+1*2=0

We add all the numbers together, and all the variables

-4^2x*2+3=0

Wy multiply elements

-8x^2+3=0

a = -8; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-8)·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-8}=\frac{0-4\sqrt{6}}{-16}
=-\frac{4\sqrt{6}}{-16}
=-\frac{\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-8}=\frac{0+4\sqrt{6}}{-16}
=\frac{4\sqrt{6}}{-16}
=\frac{\sqrt{6}}{-4}
$