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

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

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

We move all terms to the left:

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


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R



Domain of the equation: 8pp)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-8p)/64p^2+(-24p)/64p^2-24=0

We multiply all the terms by the denominator


(-8p)+(-24p)-24*64p^2=0

Wy multiply elements

-1536p^2+(-8p)+(-24p)=0

We get rid of parentheses

-1536p^2-8p-24p=0

We add all the numbers together, and all the variables

-1536p^2-32p=0

a = -1536; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-1536)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-1536}=\frac{0}{-3072}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-1536}=\frac{64}{-3072}
=-1/48
$