1/4^2x+3=32

Solution for 1/4^2x+3=32 equation:

1/4^2x+3=32

We move all terms to the left:

1/4^2x+3-(32)=0


Domain of the equation: 4^2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4^2x-29=0

We multiply all the terms by the denominator


-29*4^2x+1=0

Wy multiply elements

-116x^2+1=0

a = -116; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-116)·1
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{29}}{2*-116}=\frac{0-4\sqrt{29}}{-232}
=-\frac{4\sqrt{29}}{-232}
=-\frac{\sqrt{29}}{-58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{29}}{2*-116}=\frac{0+4\sqrt{29}}{-232}
=\frac{4\sqrt{29}}{-232}
=\frac{\sqrt{29}}{-58}
$