1/6p=1/3p+6

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

1/6p=1/3p+6

We move all terms to the left:

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


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 3p+6)!=0

p∈R


We get rid of parentheses

1/6p-1/3p-6=0

We calculate fractions


3p/18p^2+(-6p)/18p^2-6=0

We multiply all the terms by the denominator


3p+(-6p)-6*18p^2=0

Wy multiply elements

-108p^2+3p+(-6p)=0

We get rid of parentheses

-108p^2+3p-6p=0

We add all the numbers together, and all the variables

-108p^2-3p=0

a = -108; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-108)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-108}=\frac{0}{-216}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-108}=\frac{6}{-216}
=-1/36
$