-24-1/8p=p

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

-24-1/8p=p

We move all terms to the left:

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


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8p^2-192p-1=0

a = -8; b = -192; c = -1;
Δ = b2-4ac
Δ = -1922-4·(-8)·(-1)
Δ = 36832
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:

$\sqrt{\Delta}=\sqrt{36832}=\sqrt{16*2302}=\sqrt{16}*\sqrt{2302}=4\sqrt{2302}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-4\sqrt{2302}}{2*-8}=\frac{192-4\sqrt{2302}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+4\sqrt{2302}}{2*-8}=\frac{192+4\sqrt{2302}}{-16}
$