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

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

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

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-84p^2)/216p^2+72p/216p^2+108p/216p^2+7-9=0

We add all the numbers together, and all the variables

(-84p^2)/216p^2+72p/216p^2+108p/216p^2-2=0

We multiply all the terms by the denominator


(-84p^2)+72p+108p-2*216p^2=0

We add all the numbers together, and all the variables

(-84p^2)+180p-2*216p^2=0

Wy multiply elements

(-84p^2)-432p^2+180p=0

We get rid of parentheses

-84p^2-432p^2+180p=0

We add all the numbers together, and all the variables

-516p^2+180p=0

a = -516; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-516)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-516}=\frac{-360}{-1032}
=15/43
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-516}=\frac{0}{-1032}
=0
$