1/5p+2/3=1/6p

Solution for 1/5p+2/3=1/6p equation:

1/5p+2/3=1/6p

We move all terms to the left:

1/5p+2/3-(1/6p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 6p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/5p-(+1/6p)+2/3=0

We get rid of parentheses

1/5p-1/6p+2/3=0

We calculate fractions


360p^2/270p^2+54p/270p^2+(-45p)/270p^2=0

We multiply all the terms by the denominator


360p^2+54p+(-45p)=0

We get rid of parentheses

360p^2+54p-45p=0

We add all the numbers together, and all the variables

360p^2+9p=0

a = 360; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·360·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*360}=\frac{-18}{720}
=-1/40
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*360}=\frac{0}{720}
=0
$