16+3p=2/3p=5

Solution for 16+3p=2/3p=5 equation:

16+3p=2/3p=5

We move all terms to the left:

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


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3p-2/3p+16=0

We multiply all the terms by the denominator


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

Wy multiply elements

9p^2+48p-2=0

a = 9; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·9·(-2)
Δ = 2376
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:

$\sqrt{\Delta}=\sqrt{2376}=\sqrt{36*66}=\sqrt{36}*\sqrt{66}=6\sqrt{66}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{66}}{2*9}=\frac{-48-6\sqrt{66}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{66}}{2*9}=\frac{-48+6\sqrt{66}}{18}
$