1/3p-3=1/24p

Solution for 1/3p-3=1/24p equation:

1/3p-3=1/24p

We move all terms to the left:

1/3p-3-(1/24p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 24p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/3p-(+1/24p)-3=0

We get rid of parentheses

1/3p-1/24p-3=0

We calculate fractions


24p/72p^2+(-3p)/72p^2-3=0

We multiply all the terms by the denominator


24p+(-3p)-3*72p^2=0

Wy multiply elements

-216p^2+24p+(-3p)=0

We get rid of parentheses

-216p^2+24p-3p=0

We add all the numbers together, and all the variables

-216p^2+21p=0

a = -216; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-216)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-216}=\frac{-42}{-432}
=7/72
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-216}=\frac{0}{-432}
=0
$