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

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

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

We move all terms to the left:

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


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

64p^2-24p-192p-1=0

We add all the numbers together, and all the variables

64p^2-216p-1=0

a = 64; b = -216; c = -1;
Δ = b2-4ac
Δ = -2162-4·64·(-1)
Δ = 46912
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{46912}=\sqrt{64*733}=\sqrt{64}*\sqrt{733}=8\sqrt{733}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-8\sqrt{733}}{2*64}=\frac{216-8\sqrt{733}}{128}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+8\sqrt{733}}{2*64}=\frac{216+8\sqrt{733}}{128}
$