p+(1/3)p=2/3

Solution for p+(1/3)p=2/3 equation:

p+(1/3)p=2/3

We move all terms to the left:

p+(1/3)p-(2/3)=0


Domain of the equation: 3)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p+(+1/3)p-(+2/3)=0

We multiply parentheses

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

We get rid of parentheses

p^2+p-2/3=0

We multiply all the terms by the denominator


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

Wy multiply elements

3p^2+3p-2=0

a = 3; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·3·(-2)
Δ = 33
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{-(3)-\sqrt{33}}{2*3}=\frac{-3-\sqrt{33}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*3}=\frac{-3+\sqrt{33}}{6}
$