p=1/312p

Solution for p=1/312p equation:

p=1/312p

We move all terms to the left:

p-(1/312p)=0


Domain of the equation: 312p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p-(+1/312p)=0

We get rid of parentheses

p-1/312p=0

We multiply all the terms by the denominator


p*312p-1=0

Wy multiply elements

312p^2-1=0

a = 312; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·312·(-1)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*312}=\frac{0-4\sqrt{78}}{624}
=-\frac{4\sqrt{78}}{624}
=-\frac{\sqrt{78}}{156}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*312}=\frac{0+4\sqrt{78}}{624}
=\frac{4\sqrt{78}}{624}
=\frac{\sqrt{78}}{156}
$