1/2p-3-2/3p=6

Solution for 1/2p-3-2/3p=6 equation:

1/2p-3-2/3p=6

We move all terms to the left:

1/2p-3-2/3p-(6)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

1/2p-2/3p-9=0

We calculate fractions


3p/6p^2+(-4p)/6p^2-9=0

We multiply all the terms by the denominator


3p+(-4p)-9*6p^2=0

Wy multiply elements

-54p^2+3p+(-4p)=0

We get rid of parentheses

-54p^2+3p-4p=0

We add all the numbers together, and all the variables

-54p^2-1p=0

a = -54; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-54)·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*-54}=\frac{0}{-108}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-54}=\frac{2}{-108}
=-1/54
$