(1)/(3)p-8-p=4

Solution for (1)/(3)p-8-p=4 equation:

(1)/(3)p-8-p=4

We move all terms to the left:

(1)/(3)p-8-p-(4)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

-1p+1/3p-12=0

We multiply all the terms by the denominator


-1p*3p-12*3p+1=0

Wy multiply elements

-3p^2-36p+1=0

a = -3; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-3)·1
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{327}}{2*-3}=\frac{36-2\sqrt{327}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{327}}{2*-3}=\frac{36+2\sqrt{327}}{-6}
$