p/3p+16=46+2p

Solution for p/3p+16=46+2p equation:

p/3p+16=46+2p

We move all terms to the left:

p/3p+16-(46+2p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

p/3p-(2p+46)+16=0

We get rid of parentheses

p/3p-2p-46+16=0

We multiply all the terms by the denominator


p-2p*3p-46*3p+16*3p=0

Wy multiply elements

-6p^2+p-138p+48p=0

We add all the numbers together, and all the variables

-6p^2-89p=0

a = -6; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·(-6)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*-6}=\frac{0}{-12}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*-6}=\frac{178}{-12}
=-14+5/6
$