p*3^-3=p/27

Solution for p*3^-3=p/27 equation:

p*3^-3=p/27

We move all terms to the left:

p*3^-3-(p/27)=0

We add all the numbers together, and all the variables

p*3^-(+p/27)-3=0

Wy multiply elements

3p^2-(+p/27)-3=0

We get rid of parentheses

3p^2-p/27-3=0

We multiply all the terms by the denominator


3p^2*27-p-3*27=0

We add all the numbers together, and all the variables

3p^2*27-1p-81=0

Wy multiply elements

81p^2-1p-81=0

a = 81; b = -1; c = -81;
Δ = b2-4ac
Δ = -12-4·81·(-81)
Δ = 26245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{26245}}{2*81}=\frac{1-\sqrt{26245}}{162}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{26245}}{2*81}=\frac{1+\sqrt{26245}}{162}
$