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+8)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-4p*3p-8*3p-3*3p+1=0

Wy multiply elements

-12p^2-24p-9p+1=0

We add all the numbers together, and all the variables

-12p^2-33p+1=0

a = -12; b = -33; c = +1;
Δ = b2-4ac
Δ = -332-4·(-12)·1
Δ = 1137
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{-(-33)-\sqrt{1137}}{2*-12}=\frac{33-\sqrt{1137}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1137}}{2*-12}=\frac{33+\sqrt{1137}}{-24}
$