1/3p+1/2+7=7/6p+5+4

Solution for 1/3p+1/2+7=7/6p+5+4 equation:

1/3p+1/2+7=7/6p+5+4

We move all terms to the left:

1/3p+1/2+7-(7/6p+5+4)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 6p+5+4)!=0

We move all terms containing p to the left, all other terms to the right

6p+4)!=-5

p∈R


We add all the numbers together, and all the variables

1/3p-(7/6p+9)+7+1/2=0

We get rid of parentheses

1/3p-7/6p-9+7+1/2=0

We calculate fractions


108p^2/72p^2+24p/72p^2+(-84p)/72p^2-9+7=0

We add all the numbers together, and all the variables

108p^2/72p^2+24p/72p^2+(-84p)/72p^2-2=0

We multiply all the terms by the denominator


108p^2+24p+(-84p)-2*72p^2=0

Wy multiply elements

108p^2-144p^2+24p+(-84p)=0

We get rid of parentheses

108p^2-144p^2+24p-84p=0

We add all the numbers together, and all the variables

-36p^2-60p=0

a = -36; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-36)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-36}=\frac{0}{-72}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-36}=\frac{120}{-72}
=-1+2/3
$