5/16p+3=1/3p

Solution for 5/16p+3=1/3p equation:

5/16p+3=1/3p

We move all terms to the left:

5/16p+3-(1/3p)=0


Domain of the equation: 16p!=0

p!=0/16

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

5/16p-(+1/3p)+3=0

We get rid of parentheses

5/16p-1/3p+3=0

We calculate fractions


15p/48p^2+(-16p)/48p^2+3=0

We multiply all the terms by the denominator


15p+(-16p)+3*48p^2=0

Wy multiply elements

144p^2+15p+(-16p)=0

We get rid of parentheses

144p^2+15p-16p=0

We add all the numbers together, and all the variables

144p^2-1p=0

a = 144; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·144·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*144}=\frac{0}{288}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*144}=\frac{2}{288}
=1/144
$