16-3p=2/3p+p

Solution for 16-3p=2/3p+p equation:

16-3p=2/3p+p

We move all terms to the left:

16-3p-(2/3p+p)=0


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

p∈R


We add all the numbers together, and all the variables

-3p-(+p+2/3p)+16=0

We get rid of parentheses

-3p-p-2/3p+16=0

We multiply all the terms by the denominator


-3p*3p-p*3p+16*3p-2=0

Wy multiply elements

-9p^2-3p^2+48p-2=0

We add all the numbers together, and all the variables

-12p^2+48p-2=0

a = -12; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·(-12)·(-2)
Δ = 2208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{138}}{2*-12}=\frac{-48-4\sqrt{138}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{138}}{2*-12}=\frac{-48+4\sqrt{138}}{-24}
$