2p=22/3p

Solution for 2p=22/3p equation:

2p=22/3p

We move all terms to the left:

2p-(22/3p)=0


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

2p-(+22/3p)=0

We get rid of parentheses

2p-22/3p=0

We multiply all the terms by the denominator


2p*3p-22=0

Wy multiply elements

6p^2-22=0

a = 6; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·6·(-22)
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*6}=\frac{0-4\sqrt{33}}{12}
=-\frac{4\sqrt{33}}{12}
=-\frac{\sqrt{33}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*6}=\frac{0+4\sqrt{33}}{12}
=\frac{4\sqrt{33}}{12}
=\frac{\sqrt{33}}{3}
$