1/2p+84=2/3p

Solution for 1/2p+84=2/3p equation:

1/2p+84=2/3p

We move all terms to the left:

1/2p+84-(2/3p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/2p-(+2/3p)+84=0

We get rid of parentheses

1/2p-2/3p+84=0

We calculate fractions


3p/6p^2+(-4p)/6p^2+84=0

We multiply all the terms by the denominator


3p+(-4p)+84*6p^2=0

Wy multiply elements

504p^2+3p+(-4p)=0

We get rid of parentheses

504p^2+3p-4p=0

We add all the numbers together, and all the variables

504p^2-1p=0

a = 504; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·504·0
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*504}=\frac{0}{1008}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*504}=\frac{2}{1008}
=1/504
$