16-3p=2/pp+5

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

16-3p=2/pp+5

We move all terms to the left:

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


Domain of the equation: pp+5)!=0

p∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3p^2+11p-2=0

a = -3; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·(-3)·(-2)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{97}}{2*-3}=\frac{-11-\sqrt{97}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{97}}{2*-3}=\frac{-11+\sqrt{97}}{-6}
$