1/6p+1/3p=1

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

1/6p+1/3p=1

We move all terms to the left:

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


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We calculate fractions


3p/18p^2+6p/18p^2-1=0

We multiply all the terms by the denominator


3p+6p-1*18p^2=0

We add all the numbers together, and all the variables

9p-1*18p^2=0

Wy multiply elements

-18p^2+9p=0

a = -18; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-18)·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*-18}=\frac{-18}{-36}
=1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-18}=\frac{0}{-36}
=0
$