2/3p-1=1p

Solution for 2/3p-1=1p equation:

2/3p-1=1p

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1p*3p-1*3p+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}
$