p=22/3p

Solution for p=22/3p equation:

p=22/3p

We move all terms to the left:

p-(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

p-(+22/3p)=0

We get rid of parentheses

p-22/3p=0

We multiply all the terms by the denominator


p*3p-22=0

Wy multiply elements

3p^2-22=0

a = 3; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·3·(-22)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*3}=\frac{0-2\sqrt{66}}{6}
=-\frac{2\sqrt{66}}{6}
=-\frac{\sqrt{66}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*3}=\frac{0+2\sqrt{66}}{6}
=\frac{2\sqrt{66}}{6}
=\frac{\sqrt{66}}{3}
$