4^2x=163/4

Solution for 4^2x=163/4 equation:

4^2x=163/4

We move all terms to the left:

4^2x-(163/4)=0

We add all the numbers together, and all the variables

4^2x-(+163/4)=0

We get rid of parentheses

4^2x-163/4=0

We multiply all the terms by the denominator


4^2x*4-163=0

Wy multiply elements

16x^2-163=0

a = 16; b = 0; c = -163;
Δ = b2-4ac
Δ = 02-4·16·(-163)
Δ = 10432
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:

$\sqrt{\Delta}=\sqrt{10432}=\sqrt{64*163}=\sqrt{64}*\sqrt{163}=8\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{163}}{2*16}=\frac{0-8\sqrt{163}}{32}
=-\frac{8\sqrt{163}}{32}
=-\frac{\sqrt{163}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{163}}{2*16}=\frac{0+8\sqrt{163}}{32}
=\frac{8\sqrt{163}}{32}
=\frac{\sqrt{163}}{4}
$