1/3p+p=48

Solution for 1/3p+p=48 equation:

1/3p+p=48

We move all terms to the left:

1/3p+p-(48)=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+1/3p-48=0

We multiply all the terms by the denominator


p*3p-48*3p+1=0

Wy multiply elements

3p^2-144p+1=0

a = 3; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·3·1
Δ = 20724
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:

$\sqrt{\Delta}=\sqrt{20724}=\sqrt{4*5181}=\sqrt{4}*\sqrt{5181}=2\sqrt{5181}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{5181}}{2*3}=\frac{144-2\sqrt{5181}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{5181}}{2*3}=\frac{144+2\sqrt{5181}}{6}
$