1/3p-3=4p=8

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

1/3p-3=4p=8

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

-4p+1/3p-3=0

We multiply all the terms by the denominator


-4p*3p-3*3p+1=0

Wy multiply elements

-12p^2-9p+1=0

a = -12; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-12)·1
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{129}}{2*-12}=\frac{9-\sqrt{129}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*-12}=\frac{9+\sqrt{129}}{-24}
$