1/3p-5=1/4p

Solution for 1/3p-5=1/4p equation:

1/3p-5=1/4p

We move all terms to the left:

1/3p-5-(1/4p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 4p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/3p-(+1/4p)-5=0

We get rid of parentheses

1/3p-1/4p-5=0

We calculate fractions


4p/12p^2+(-3p)/12p^2-5=0

We multiply all the terms by the denominator


4p+(-3p)-5*12p^2=0

Wy multiply elements

-60p^2+4p+(-3p)=0

We get rid of parentheses

-60p^2+4p-3p=0

We add all the numbers together, and all the variables

-60p^2+p=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·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*-60}=\frac{-2}{-120}
=1/60
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120}
=0
$