p+6/6p=1+p+6/2p

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

p+6/6p=1+p+6/2p

We move all terms to the left:

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


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


p-p+12p/12p^2+(-36p)/12p^2-1=0

We add all the numbers together, and all the variables

12p/12p^2+(-36p)/12p^2-1=0

We multiply all the terms by the denominator


12p+(-36p)-1*12p^2=0

Wy multiply elements

-12p^2+12p+(-36p)=0

We get rid of parentheses

-12p^2+12p-36p=0

We add all the numbers together, and all the variables

-12p^2-24p=0

a = -12; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-12)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-12}=\frac{0}{-24}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-12}=\frac{48}{-24}
=-2
$