31/8p+3/4p=259/12

Solution for 31/8p+3/4p=259/12 equation:

31/8p+3/4p=259/12

We move all terms to the left:

31/8p+3/4p-(259/12)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R



Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

31/8p+3/4p-(+259/12)=0

We get rid of parentheses

31/8p+3/4p-259/12=0

We calculate fractions


(-33152p^2)/384p^2+1488p/384p^2+288p/384p^2=0

We multiply all the terms by the denominator


(-33152p^2)+1488p+288p=0

We add all the numbers together, and all the variables

(-33152p^2)+1776p=0

We get rid of parentheses

-33152p^2+1776p=0

a = -33152; b = 1776; c = 0;
Δ = b2-4ac
Δ = 17762-4·(-33152)·0
Δ = 3154176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3154176}=1776$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1776)-1776}{2*-33152}=\frac{-3552}{-66304}
=3/56
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1776)+1776}{2*-33152}=\frac{0}{-66304}
=0
$