4p=81/p

Solution for 4p=81/p equation:

4p=81/p

We move all terms to the left:

4p-(81/p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

4p-(+81/p)=0

We get rid of parentheses

4p-81/p=0

We multiply all the terms by the denominator


4p*p-81=0

Wy multiply elements

4p^2-81=0

a = 4; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·4·(-81)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*4}=\frac{-36}{8}
=-4+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*4}=\frac{36}{8}
=4+1/2
$