1/6p-2=1/3p+8

Solution for 1/6p-2=1/3p+8 equation:

1/6p-2=1/3p+8

We move all terms to the left:

1/6p-2-(1/3p+8)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 3p+8)!=0

p∈R


We get rid of parentheses

1/6p-1/3p-8-2=0

We calculate fractions


3p/18p^2+(-6p)/18p^2-8-2=0

We add all the numbers together, and all the variables

3p/18p^2+(-6p)/18p^2-10=0

We multiply all the terms by the denominator


3p+(-6p)-10*18p^2=0

Wy multiply elements

-180p^2+3p+(-6p)=0

We get rid of parentheses

-180p^2+3p-6p=0

We add all the numbers together, and all the variables

-180p^2-3p=0

a = -180; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-180)·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*-180}=\frac{0}{-360}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-180}=\frac{6}{-360}
=-1/60
$