-24-1/8p=38p

Solution for -24-1/8p=38p equation:

-24-1/8p=38p

We move all terms to the left:

-24-1/8p-(38p)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R


We add all the numbers together, and all the variables

-38p-1/8p-24=0

We multiply all the terms by the denominator


-38p*8p-24*8p-1=0

Wy multiply elements

-304p^2-192p-1=0

a = -304; b = -192; c = -1;
Δ = b2-4ac
Δ = -1922-4·(-304)·(-1)
Δ = 35648
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:

$\sqrt{\Delta}=\sqrt{35648}=\sqrt{64*557}=\sqrt{64}*\sqrt{557}=8\sqrt{557}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-8\sqrt{557}}{2*-304}=\frac{192-8\sqrt{557}}{-608}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+8\sqrt{557}}{2*-304}=\frac{192+8\sqrt{557}}{-608}
$