2/3*p=1/2*p+3

Solution for 2/3*p=1/2*p+3 equation:

2/3p=1/2p+3

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p+3)!=0

p∈R


We get rid of parentheses

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

We calculate fractions


4p/6p^2+(-3p)/6p^2-3=0

We multiply all the terms by the denominator


4p+(-3p)-3*6p^2=0

Wy multiply elements

-18p^2+4p+(-3p)=0

We get rid of parentheses

-18p^2+4p-3p=0

We add all the numbers together, and all the variables

-18p^2+p=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-18}=\frac{-2}{-36}
=1/18
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36}
=0
$