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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


72p^2/108p^2+54p/108p^2+(-126p)/108p^2-9+7=0

We add all the numbers together, and all the variables

72p^2/108p^2+54p/108p^2+(-126p)/108p^2-2=0

We multiply all the terms by the denominator


72p^2+54p+(-126p)-2*108p^2=0

Wy multiply elements

72p^2-216p^2+54p+(-126p)=0

We get rid of parentheses

72p^2-216p^2+54p-126p=0

We add all the numbers together, and all the variables

-144p^2-72p=0

a = -144; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-144)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-144}=\frac{0}{-288}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-144}=\frac{144}{-288}
=-1/2
$