2/3p-4=1/4p+8

Solution for 2/3p-4=1/4p+8 equation:

2/3p-4=1/4p+8

We move all terms to the left:

2/3p-4-(1/4p+8)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 4p+8)!=0

p∈R


We get rid of parentheses

2/3p-1/4p-8-4=0

We calculate fractions


8p/12p^2+(-3p)/12p^2-8-4=0

We add all the numbers together, and all the variables

8p/12p^2+(-3p)/12p^2-12=0

We multiply all the terms by the denominator


8p+(-3p)-12*12p^2=0

Wy multiply elements

-144p^2+8p+(-3p)=0

We get rid of parentheses

-144p^2+8p-3p=0

We add all the numbers together, and all the variables

-144p^2+5p=0

a = -144; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-144)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-144}=\frac{-10}{-288}
=5/144
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-144}=\frac{0}{-288}
=0
$