16-3p=2p/3p+5

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

16-3p=2p/3p+5

We move all terms to the left:

16-3p-(2p/3p+5)=0


Domain of the equation: 3p+5)!=0

p∈R


We get rid of parentheses

-3p-2p/3p-5+16=0

We multiply all the terms by the denominator


-3p*3p-2p-5*3p+16*3p=0

We add all the numbers together, and all the variables

-2p-3p*3p-5*3p+16*3p=0

Wy multiply elements

-9p^2-2p-15p+48p=0

We add all the numbers together, and all the variables

-9p^2+31p=0

a = -9; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-9)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-9}=\frac{-62}{-18}
=3+4/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-9}=\frac{0}{-18}
=0
$