(31/4)p=2/12

Solution for (31/4)p=2/12 equation:

(31/4)p=2/12

We move all terms to the left:

(31/4)p-(2/12)=0


Domain of the equation: 4)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(+31/4)p-(+2/12)=0

We multiply parentheses

31p^2-(+2/12)=0

We get rid of parentheses

31p^2-2/12=0

We multiply all the terms by the denominator


31p^2*12-2=0

Wy multiply elements

372p^2-2=0

a = 372; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·372·(-2)
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{186}}{2*372}=\frac{0-4\sqrt{186}}{744}
=-\frac{4\sqrt{186}}{744}
=-\frac{\sqrt{186}}{186}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{186}}{2*372}=\frac{0+4\sqrt{186}}{744}
=\frac{4\sqrt{186}}{744}
=\frac{\sqrt{186}}{186}
$