2/3p+6=7/6p

Solution for 2/3p+6=7/6p equation:

2/3p+6=7/6p

We move all terms to the left:

2/3p+6-(7/6p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 6p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

2/3p-(+7/6p)+6=0

We get rid of parentheses

2/3p-7/6p+6=0

We calculate fractions


12p/18p^2+(-21p)/18p^2+6=0

We multiply all the terms by the denominator


12p+(-21p)+6*18p^2=0

Wy multiply elements

108p^2+12p+(-21p)=0

We get rid of parentheses

108p^2+12p-21p=0

We add all the numbers together, and all the variables

108p^2-9p=0

a = 108; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·108·0
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*108}=\frac{0}{216}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*108}=\frac{18}{216}
=1/12
$