p-36=8-1/3p

Solution for p-36=8-1/3p equation:

p-36=8-1/3p

We move all terms to the left:

p-36-(8-1/3p)=0


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p-(-1/3p+8)-36=0

We get rid of parentheses

p+1/3p-8-36=0

We multiply all the terms by the denominator


p*3p-8*3p-36*3p+1=0

Wy multiply elements

3p^2-24p-108p+1=0

We add all the numbers together, and all the variables

3p^2-132p+1=0

a = 3; b = -132; c = +1;
Δ = b2-4ac
Δ = -1322-4·3·1
Δ = 17412
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:

$\sqrt{\Delta}=\sqrt{17412}=\sqrt{4*4353}=\sqrt{4}*\sqrt{4353}=2\sqrt{4353}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4353}}{2*3}=\frac{132-2\sqrt{4353}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4353}}{2*3}=\frac{132+2\sqrt{4353}}{6}
$