-24-1/p=3/8p

Solution for -24-1/p=3/8p equation:

-24-1/p=3/8p

We move all terms to the left:

-24-1/p-(3/8p)=0


Domain of the equation: p!=0

p∈R



Domain of the equation: 8p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-1/p-(+3/8p)-24=0

We get rid of parentheses

-1/p-3/8p-24=0

We calculate fractions


(-8p)/8p^2+(-3p)/8p^2-24=0

We multiply all the terms by the denominator


(-8p)+(-3p)-24*8p^2=0

Wy multiply elements

-192p^2+(-8p)+(-3p)=0

We get rid of parentheses

-192p^2-8p-3p=0

We add all the numbers together, and all the variables

-192p^2-11p=0

a = -192; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-192)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-192}=\frac{0}{-384}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-192}=\frac{22}{-384}
=-11/192
$