16^-3p-2=1/4^p-2

Solution for 16^-3p-2=1/4^p-2 equation:

16^-3p-2=1/4^p-2

We move all terms to the left:

16^-3p-2-(1/4^p-2)=0


Domain of the equation: 4^p-2)!=0

p∈R


We add all the numbers together, and all the variables

-3p-(1/4^p-2)=0

We get rid of parentheses

-3p-1/4^p+2=0

We multiply all the terms by the denominator


-3p*4^p+2*4^p-1=0

Wy multiply elements

-12p^2+8p-1=0

a = -12; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-12)·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*-12}=\frac{-12}{-24}
=1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-12}=\frac{-4}{-24}
=1/6
$